Coupling RBF-based meshless method and Landweber iteration algorithm for approximating a space-dependent source term in a time fractional diffusion equation
The problem of determining a space-dependent source term in a time fractional diffusion equation is considered from the measured data at the final time. To find an approximation of the source term, a methodology involving minimization of the cost functional is applied. Also, in order to construct th...
Saved in:
| Published in | Journal of computational and applied mathematics Vol. 417; p. 114531 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.01.2023
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | The problem of determining a space-dependent source term in a time fractional diffusion equation is considered from the measured data at the final time. To find an approximation of the source term, a methodology involving minimization of the cost functional is applied. Also, in order to construct the Landweber iteration algorithm, an explicit formula for the gradient of the cost functional J is given via the solution of an adjoint problem. The resulting adjoint problem is treated by a radial basis function method for spatial dimension and a finite difference scheme for the time fractional derivative followed by an iterative domain decomposition method to achieve a desired accuracy. In addition, Lipschitz continuity of the gradient of the cost functional, monotonicity and convergence of Landweber iteration algorithm are proved. At the end, a numerical example is given to show the validation of the iterative algorithm. |
|---|---|
| AbstractList | The problem of determining a space-dependent source term in a time fractional diffusion equation is considered from the measured data at the final time. To find an approximation of the source term, a methodology involving minimization of the cost functional is applied. Also, in order to construct the Landweber iteration algorithm, an explicit formula for the gradient of the cost functional J is given via the solution of an adjoint problem. The resulting adjoint problem is treated by a radial basis function method for spatial dimension and a finite difference scheme for the time fractional derivative followed by an iterative domain decomposition method to achieve a desired accuracy. In addition, Lipschitz continuity of the gradient of the cost functional, monotonicity and convergence of Landweber iteration algorithm are proved. At the end, a numerical example is given to show the validation of the iterative algorithm. |
| ArticleNumber | 114531 |
| Author | Salehi Shayegan, Amir Hossein |
| Author_xml | – sequence: 1 givenname: Amir Hossein surname: Salehi Shayegan fullname: Salehi Shayegan, Amir Hossein email: ah.salehi@mail.kntu.ac.ir organization: Mathematics Department, Faculty of Basic Science, Khatam-ol-Anbia (PBU) University, Tehran, Iran |
| BookMark | eNp9kMtOAyEUhompiW31AdzxAjPC3JjGlTZWTZqYGF0TBg4tzcwwAvXyLj6sjHXlopvDSf58P_DN0KS3PSB0SUlKCa2udqkUXZqRLEspLcqcnqAprdkioYzVEzQlOWMJKTJ2hmbe7wgh1YIWU_S9tPuhNf0GP9-ukkZ4ULgDv23B-7iErVVY9Aqv4_iABhw2AZwIxvZYtBvrTNh2WFuHxTA4-2m6mMU2gf0gJCQKBugV9AF7u3cScKQ7bCKMg-kAayfkWCZarIzWez8Ww9v-94ZzdKpF6-Hi75yj19Xdy_IhWT_dPy5v1onMMhYSpUtRa8G0olAqQjOhakWbImrIK8l0lZVFWUjWxFADbRZ1oWSui1ooWkHN8jlih17prPcONJcm_L4gOGFaTgkfJfMdj5L5KJkfJEeS_iMHFxW4r6PM9YGB-KV3A457aaCXoIwDGbiy5gj9A8uNmx4 |
| CitedBy_id | crossref_primary_10_1007_s10915_024_02634_x crossref_primary_10_1515_cmam_2022_0178 crossref_primary_10_1016_j_cam_2023_115094 crossref_primary_10_1007_s12190_024_02361_4 crossref_primary_10_1177_1045389X241233800 crossref_primary_10_1016_j_cam_2023_115214 crossref_primary_10_1080_10407790_2024_2306264 |
| Cites_doi | 10.2478/s13540-011-0028-2 10.1002/num.20112 10.1007/s11075-015-0065-8 10.1016/S0955-7997(03)00102-4 10.1002/mma.4468 10.1016/0898-1221(90)90271-K 10.1016/S0022-247X(02)00155-5 10.4208/cicp.020709.221209a 10.1080/17415977.2017.1417406 10.1023/A:1018919824891 10.1137/080714130 10.1515/jiip-2019-0006 10.1002/cpa.3160440203 10.1002/mma.4719 10.1007/s11075-020-00952-3 10.1080/17415977.2017.1384826 10.1016/j.jmaa.2006.08.018 10.1002/num.22081 10.1007/s10492-014-0081-3 10.3934/mcrf.2011.1.509 10.1016/j.jmva.2012.09.007 10.1142/9789812708632_0024 10.1088/0266-5611/10/5/009 10.1002/num.20169 10.1088/0266-5611/12/3/002 10.1016/0898-1221(90)90270-T 10.1016/j.camwa.2018.03.014 10.1007/s10092-016-0181-4 10.1002/cnm.653 |
| ContentType | Journal Article |
| Copyright | 2022 Elsevier B.V. |
| Copyright_xml | – notice: 2022 Elsevier B.V. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.cam.2022.114531 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1879-1778 |
| ExternalDocumentID | 10_1016_j_cam_2022_114531 S0377042722002618 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAXUO ABAOU ABJNI ABMAC ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE AEBSH AEKER AENEX AFKWA AFTJW AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR AXJTR BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA HVGLF IHE IXB J1W KOM LG9 M26 M41 MHUIS MO0 N9A O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 RNS ROL RPZ SDF SDG SDP SES SPC SPCBC SSW T5K TN5 UPT XPP YQT ZMT ~02 ~G- 29K 5VS AAFWJ AAQFI AAQXK AATTM AAXKI AAYWO AAYXX ABDPE ABEFU ABFNM ABWVN ABXDB ACRPL ACVFH ADCNI ADMUD ADNMO ADVLN AEIPS AEUPX AEXQZ AFJKZ AFPUW AGCQF AGHFR AGQPQ AGRNS AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN BNPGV CITATION D-I EJD FGOYB G-2 HZ~ NHB R2- RIG SEW SSH SSZ WUQ ZY4 |
| ID | FETCH-LOGICAL-c227t-df5a8fa7fd1e5d012ad8d1b445336c7f625454c7b5d0fe1b984dc3f48ad16e873 |
| IEDL.DBID | .~1 |
| ISSN | 0377-0427 |
| IngestDate | Thu Apr 24 22:59:00 EDT 2025 Tue Jul 01 04:27:18 EDT 2025 Fri Feb 23 02:39:00 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Radial basis functions Inverse source problem 35R30 Meshless method Time fractional diffusion equation Landweber iteration algorithm 65M32 Lipschitz continuity |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c227t-df5a8fa7fd1e5d012ad8d1b445336c7f625454c7b5d0fe1b984dc3f48ad16e873 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_cam_2022_114531 crossref_primary_10_1016_j_cam_2022_114531 elsevier_sciencedirect_doi_10_1016_j_cam_2022_114531 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2023-01-01 2023-01-00 |
| PublicationDateYYYYMMDD | 2023-01-01 |
| PublicationDate_xml | – month: 01 year: 2023 text: 2023-01-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Journal of computational and applied mathematics |
| PublicationYear | 2023 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Hasanov (b3) 2007; 330 Zeghal (b7) 2002; 272 Torebek, Tapdigoglu (b13) 2017; 40 Liu, Gu (b14) 2005 Kinash, Janno (b11) 2018; 41 Ford, Xiao, Yan (b25) 2011; 14 Esmaeilbeigi, Garmanjani (b18) 2016; 32 Deng (b30) 2008; 47 Isakov (b5) 1991; 54 Cheng, Yuan, Liang (b9) 2020; 28 Kansa (b16) 1990; 19 Kaya (b6) 2014; 59 Hon, Wei (b22) 2004; 28 Sakamoto, Yamamoto (b12) 2011; 1 Shanazari, Banei (b15) 2021; 86 Salehi Shayegan, Zakeri (b27) 2018; 26 Fasshuaer (b32) 2007; 6 Li (b23) 2004; 20 Feng, Zhuang, Liu, Turner, Gu (b31) 2016; 72 Li, Xu (b26) 2010; 8 Ervin, Roop (b29) 2007; 23 Can, Luc, Baleanu, Zhou, Long (b8) 2020 Buhmann (b33) 2003 Esmaeilbeigi, Garmanjani (b19) 2017; 54 Furati, Iyiola, Kirane (b10) 2014; 249 Kansa (b17) 1990; 19 Choulli, Yamamoto (b2) 1996; 12 Hasanov Hasanoglu, Romanov (b4) 2017 Fasshuaer (b20) 1999; 11 Ervin, Roop (b28) 2006; 22 Wang, Ran (b34) 2018; 26 Valencia, Yuan (b24) 2013; 116 Chulli (b1) 1994; 10 Garmanjani, Cavoretto, Esmaeilbeigi (b21) 2018; 75 Ervin (10.1016/j.cam.2022.114531_b28) 2006; 22 Kansa (10.1016/j.cam.2022.114531_b16) 1990; 19 Zeghal (10.1016/j.cam.2022.114531_b7) 2002; 272 Buhmann (10.1016/j.cam.2022.114531_b33) 2003 Furati (10.1016/j.cam.2022.114531_b10) 2014; 249 Kaya (10.1016/j.cam.2022.114531_b6) 2014; 59 Chulli (10.1016/j.cam.2022.114531_b1) 1994; 10 Wang (10.1016/j.cam.2022.114531_b34) 2018; 26 Salehi Shayegan (10.1016/j.cam.2022.114531_b27) 2018; 26 Fasshuaer (10.1016/j.cam.2022.114531_b32) 2007; 6 Torebek (10.1016/j.cam.2022.114531_b13) 2017; 40 Garmanjani (10.1016/j.cam.2022.114531_b21) 2018; 75 Choulli (10.1016/j.cam.2022.114531_b2) 1996; 12 Kinash (10.1016/j.cam.2022.114531_b11) 2018; 41 Valencia (10.1016/j.cam.2022.114531_b24) 2013; 116 Li (10.1016/j.cam.2022.114531_b26) 2010; 8 Hasanov Hasanoglu (10.1016/j.cam.2022.114531_b4) 2017 Liu (10.1016/j.cam.2022.114531_b14) 2005 Li (10.1016/j.cam.2022.114531_b23) 2004; 20 Isakov (10.1016/j.cam.2022.114531_b5) 1991; 54 Hasanov (10.1016/j.cam.2022.114531_b3) 2007; 330 Can (10.1016/j.cam.2022.114531_b8) 2020 Fasshuaer (10.1016/j.cam.2022.114531_b20) 1999; 11 Hon (10.1016/j.cam.2022.114531_b22) 2004; 28 Deng (10.1016/j.cam.2022.114531_b30) 2008; 47 Feng (10.1016/j.cam.2022.114531_b31) 2016; 72 Sakamoto (10.1016/j.cam.2022.114531_b12) 2011; 1 Ervin (10.1016/j.cam.2022.114531_b29) 2007; 23 Cheng (10.1016/j.cam.2022.114531_b9) 2020; 28 Esmaeilbeigi (10.1016/j.cam.2022.114531_b18) 2016; 32 Ford (10.1016/j.cam.2022.114531_b25) 2011; 14 Esmaeilbeigi (10.1016/j.cam.2022.114531_b19) 2017; 54 Shanazari (10.1016/j.cam.2022.114531_b15) 2021; 86 Kansa (10.1016/j.cam.2022.114531_b17) 1990; 19 |
| References_xml | – volume: 10 start-page: 1123 year: 1994 end-page: 1132 ident: b1 article-title: An inverse problem for a semilinear parabolic equation publication-title: Inverse Problems – volume: 86 start-page: 1747 year: 2021 end-page: 1767 ident: b15 article-title: A meshfree method with a non-overlapping domain decomposition method based on TPS for solving the forward–backward heat equation in two-dimension publication-title: Numer. Algorithms – volume: 22 start-page: 558 year: 2006 end-page: 576 ident: b28 article-title: Variational formulation for the stationary fractional advection dispersion equation publication-title: Numer. Methods Partial Differential Equations – volume: 272 start-page: 240 year: 2002 end-page: 248 ident: b7 article-title: Existence result for inverse problems associated with a nonlinear parabolic equation publication-title: J. Math. Anal. Appl. – volume: 28 start-page: 489 year: 2004 end-page: 495 ident: b22 article-title: A fundamental solution method for inverse heat conduction problem publication-title: Eng. Anal. Bound. Elem. – volume: 28 start-page: 17 year: 2020 end-page: 32 ident: b9 article-title: Inverse source problem for a distributed-order time fractional diffusion equation publication-title: J. Inverse Ill-Posed Probl. – volume: 19 start-page: 127 year: 1990 end-page: 145 ident: b16 article-title: Multiquadrics, a scattered data approximation scheme with applications to computational fluid dynamics-I. Surface approximations and partial derivatives estimates publication-title: Comput. Math. Appl. – start-page: 18 year: 2020 ident: b8 article-title: Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel publication-title: Adv. Difference Equ. – volume: 32 start-page: 1622 year: 2016 end-page: 1646 ident: b18 article-title: A shift-adaptive meshfree method for solving a class of initial–boundary value problems with moving boundaries in one-dimensional domain publication-title: Numer. Methods Partial Differential Equations – volume: 8 start-page: 1016 year: 2010 end-page: 1051 ident: b26 article-title: Existence and uniqueness of the weak solution of the space–time fractional diffusion equation and a spectral method approximation publication-title: Commun. Comput. Phys. – year: 2005 ident: b14 article-title: An Introduction to Meshfree Methods and their Programming – volume: 23 start-page: 256 year: 2007 end-page: 281 ident: b29 article-title: Variational solution of fractional advection dispersion equations on bounded domains in publication-title: Numer. Methods Partial Differential Equations – volume: 54 start-page: 185 year: 1991 end-page: 209 ident: b5 article-title: Inverse parabolic problems with the final overdetermination publication-title: Comm. Pure Appl. Math. – volume: 59 start-page: 715 year: 2014 end-page: 728 ident: b6 article-title: Determination of the unknown source term in a linear parabolic problem from the measured data at the final time publication-title: Appl. Math. – volume: 47 start-page: 204 year: 2008 end-page: 226 ident: b30 article-title: Finite element method for the space and time fractional Fokker–Planck equation publication-title: SIAM J. Numer. Anal. – volume: 19 start-page: 147 year: 1990 end-page: 161 ident: b17 article-title: Multiquadrics, a scattered data approximation scheme with applications to computational fluid dynamics-II. Solutions to parabolic, hyper-bolic and elliptic partial differential equations publication-title: Comput. Math. Appl. – volume: 330 start-page: 766 year: 2007 end-page: 779 ident: b3 article-title: Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: Weak solution approach publication-title: J. Math. Anal. Appl. – volume: 26 start-page: 1130 year: 2018 end-page: 1154 ident: b27 article-title: A numerical method for determining a quasi solution of a backward time-fractional diffusion equation publication-title: Inverse Probl. Sci. Eng. – volume: 12 start-page: 195 year: 1996 end-page: 205 ident: b2 article-title: Generic well-posedness of an inverse parabolic problem-the Hölder-space approach publication-title: Inverse Problems – volume: 54 start-page: 155 year: 2017 end-page: 166 ident: b19 article-title: Gaussian radial basis function interpolant for the different data sites and basis centers publication-title: Calcolo – volume: 1 start-page: 509 year: 2011 end-page: 518 ident: b12 article-title: Inverse source problem with a final overdetermination for a fractional diffusion equation publication-title: Math. Control Relat. Fields – year: 2003 ident: b33 article-title: Radial Basis Functions: Theory and Implementations – volume: 20 start-page: 51 year: 2004 end-page: 61 ident: b23 article-title: A radial basis meshless method for solving inverse boundary value problems publication-title: Commun. Numer. Methods Eng. – year: 2017 ident: b4 article-title: Introduction to Inverse Problems for Differential Equations – volume: 249 start-page: 24 year: 2014 end-page: 31 ident: b10 article-title: An inverse problem for a generalized fractional diffusion publication-title: Appl. Math. Comput. – volume: 116 start-page: 92 year: 2013 end-page: 108 ident: b24 article-title: Radial basis function regularization for linear inverse problems with random noise publication-title: J. Multivariate Anal. – volume: 26 start-page: 1509 year: 2018 end-page: 1521 ident: b34 article-title: An iterative method for an inverse source problem of time-fractional diffusion equation publication-title: Inverse Probl. Sci. Eng. – volume: 75 start-page: 4066 year: 2018 end-page: 4090 ident: b21 article-title: A RBF partition of unity collocation method based on finite difference for initial–boundary value problems publication-title: Comput. Math. Appl. – volume: 14 start-page: 454 year: 2011 end-page: 474 ident: b25 article-title: A finite element method for time fractional partial differential equations publication-title: Fract. Calc. Appl. Anal. – volume: 41 start-page: 1925 year: 2018 end-page: 1943 ident: b11 article-title: Inverse problems for a perturbed time fractional diffusion equation with final overdetermination publication-title: Math. Methods Appl. Sci. – volume: 72 start-page: 749 year: 2016 end-page: 767 ident: b31 article-title: Finite element method for space–time fractional diffusion equation publication-title: Numer. Algorithms – volume: 6 year: 2007 ident: b32 article-title: Meshfree approximation methods with MATLAB publication-title: Interdiscip. Math. Sci. – volume: 11 start-page: 139 year: 1999 end-page: 159 ident: b20 article-title: Solving differential equationswith radial basis functions: multilevel methods and smoothing publication-title: Adv. Comput. Math. – volume: 40 start-page: 6468 year: 2017 end-page: 6479 ident: b13 article-title: Some inverse problems for the nonlocal heat equation with Caputo fractional derivative publication-title: Math. Methods Appl. Sci. – start-page: 18 issue: 210 year: 2020 ident: 10.1016/j.cam.2022.114531_b8 article-title: Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel publication-title: Adv. Difference Equ. – volume: 14 start-page: 454 issue: 3 year: 2011 ident: 10.1016/j.cam.2022.114531_b25 article-title: A finite element method for time fractional partial differential equations publication-title: Fract. Calc. Appl. Anal. doi: 10.2478/s13540-011-0028-2 – volume: 22 start-page: 558 issue: 3 year: 2006 ident: 10.1016/j.cam.2022.114531_b28 article-title: Variational formulation for the stationary fractional advection dispersion equation publication-title: Numer. Methods Partial Differential Equations doi: 10.1002/num.20112 – volume: 72 start-page: 749 issue: 3 year: 2016 ident: 10.1016/j.cam.2022.114531_b31 article-title: Finite element method for space–time fractional diffusion equation publication-title: Numer. Algorithms doi: 10.1007/s11075-015-0065-8 – volume: 28 start-page: 489 year: 2004 ident: 10.1016/j.cam.2022.114531_b22 article-title: A fundamental solution method for inverse heat conduction problem publication-title: Eng. Anal. Bound. Elem. doi: 10.1016/S0955-7997(03)00102-4 – volume: 40 start-page: 6468 issue: 18 year: 2017 ident: 10.1016/j.cam.2022.114531_b13 article-title: Some inverse problems for the nonlocal heat equation with Caputo fractional derivative publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.4468 – volume: 19 start-page: 147 year: 1990 ident: 10.1016/j.cam.2022.114531_b17 article-title: Multiquadrics, a scattered data approximation scheme with applications to computational fluid dynamics-II. Solutions to parabolic, hyper-bolic and elliptic partial differential equations publication-title: Comput. Math. Appl. doi: 10.1016/0898-1221(90)90271-K – volume: 272 start-page: 240 issue: 1 year: 2002 ident: 10.1016/j.cam.2022.114531_b7 article-title: Existence result for inverse problems associated with a nonlinear parabolic equation publication-title: J. Math. Anal. Appl. doi: 10.1016/S0022-247X(02)00155-5 – volume: 8 start-page: 1016 issue: 5 year: 2010 ident: 10.1016/j.cam.2022.114531_b26 article-title: Existence and uniqueness of the weak solution of the space–time fractional diffusion equation and a spectral method approximation publication-title: Commun. Comput. Phys. doi: 10.4208/cicp.020709.221209a – volume: 26 start-page: 1509 issue: 10 year: 2018 ident: 10.1016/j.cam.2022.114531_b34 article-title: An iterative method for an inverse source problem of time-fractional diffusion equation publication-title: Inverse Probl. Sci. Eng. doi: 10.1080/17415977.2017.1417406 – year: 2017 ident: 10.1016/j.cam.2022.114531_b4 – volume: 11 start-page: 139 issue: 2 year: 1999 ident: 10.1016/j.cam.2022.114531_b20 article-title: Solving differential equationswith radial basis functions: multilevel methods and smoothing publication-title: Adv. Comput. Math. doi: 10.1023/A:1018919824891 – volume: 47 start-page: 204 issue: 1 year: 2008 ident: 10.1016/j.cam.2022.114531_b30 article-title: Finite element method for the space and time fractional Fokker–Planck equation publication-title: SIAM J. Numer. Anal. doi: 10.1137/080714130 – volume: 28 start-page: 17 issue: 1 year: 2020 ident: 10.1016/j.cam.2022.114531_b9 article-title: Inverse source problem for a distributed-order time fractional diffusion equation publication-title: J. Inverse Ill-Posed Probl. doi: 10.1515/jiip-2019-0006 – volume: 54 start-page: 185 year: 1991 ident: 10.1016/j.cam.2022.114531_b5 article-title: Inverse parabolic problems with the final overdetermination publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.3160440203 – year: 2003 ident: 10.1016/j.cam.2022.114531_b33 – volume: 41 start-page: 1925 issue: 5 year: 2018 ident: 10.1016/j.cam.2022.114531_b11 article-title: Inverse problems for a perturbed time fractional diffusion equation with final overdetermination publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.4719 – volume: 86 start-page: 1747 issue: 4 year: 2021 ident: 10.1016/j.cam.2022.114531_b15 article-title: A meshfree method with a non-overlapping domain decomposition method based on TPS for solving the forward–backward heat equation in two-dimension publication-title: Numer. Algorithms doi: 10.1007/s11075-020-00952-3 – volume: 26 start-page: 1130 issue: 8 year: 2018 ident: 10.1016/j.cam.2022.114531_b27 article-title: A numerical method for determining a quasi solution of a backward time-fractional diffusion equation publication-title: Inverse Probl. Sci. Eng. doi: 10.1080/17415977.2017.1384826 – volume: 330 start-page: 766 issue: 2 year: 2007 ident: 10.1016/j.cam.2022.114531_b3 article-title: Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: Weak solution approach publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2006.08.018 – volume: 249 start-page: 24 year: 2014 ident: 10.1016/j.cam.2022.114531_b10 article-title: An inverse problem for a generalized fractional diffusion publication-title: Appl. Math. Comput. – volume: 32 start-page: 1622 issue: 6 year: 2016 ident: 10.1016/j.cam.2022.114531_b18 article-title: A shift-adaptive meshfree method for solving a class of initial–boundary value problems with moving boundaries in one-dimensional domain publication-title: Numer. Methods Partial Differential Equations doi: 10.1002/num.22081 – volume: 59 start-page: 715 issue: 6 year: 2014 ident: 10.1016/j.cam.2022.114531_b6 article-title: Determination of the unknown source term in a linear parabolic problem from the measured data at the final time publication-title: Appl. Math. doi: 10.1007/s10492-014-0081-3 – volume: 1 start-page: 509 issue: 4 year: 2011 ident: 10.1016/j.cam.2022.114531_b12 article-title: Inverse source problem with a final overdetermination for a fractional diffusion equation publication-title: Math. Control Relat. Fields doi: 10.3934/mcrf.2011.1.509 – volume: 116 start-page: 92 year: 2013 ident: 10.1016/j.cam.2022.114531_b24 article-title: Radial basis function regularization for linear inverse problems with random noise publication-title: J. Multivariate Anal. doi: 10.1016/j.jmva.2012.09.007 – volume: 6 year: 2007 ident: 10.1016/j.cam.2022.114531_b32 article-title: Meshfree approximation methods with MATLAB publication-title: Interdiscip. Math. Sci. doi: 10.1142/9789812708632_0024 – volume: 10 start-page: 1123 year: 1994 ident: 10.1016/j.cam.2022.114531_b1 article-title: An inverse problem for a semilinear parabolic equation publication-title: Inverse Problems doi: 10.1088/0266-5611/10/5/009 – volume: 23 start-page: 256 issue: 2 year: 2007 ident: 10.1016/j.cam.2022.114531_b29 article-title: Variational solution of fractional advection dispersion equations on bounded domains in Rd publication-title: Numer. Methods Partial Differential Equations doi: 10.1002/num.20169 – volume: 12 start-page: 195 issue: 3 year: 1996 ident: 10.1016/j.cam.2022.114531_b2 article-title: Generic well-posedness of an inverse parabolic problem-the Hölder-space approach publication-title: Inverse Problems doi: 10.1088/0266-5611/12/3/002 – year: 2005 ident: 10.1016/j.cam.2022.114531_b14 – volume: 19 start-page: 127 year: 1990 ident: 10.1016/j.cam.2022.114531_b16 article-title: Multiquadrics, a scattered data approximation scheme with applications to computational fluid dynamics-I. Surface approximations and partial derivatives estimates publication-title: Comput. Math. Appl. doi: 10.1016/0898-1221(90)90270-T – volume: 75 start-page: 4066 issue: 11 year: 2018 ident: 10.1016/j.cam.2022.114531_b21 article-title: A RBF partition of unity collocation method based on finite difference for initial–boundary value problems publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2018.03.014 – volume: 54 start-page: 155 issue: 1 year: 2017 ident: 10.1016/j.cam.2022.114531_b19 article-title: Gaussian radial basis function interpolant for the different data sites and basis centers publication-title: Calcolo doi: 10.1007/s10092-016-0181-4 – volume: 20 start-page: 51 issue: 1 year: 2004 ident: 10.1016/j.cam.2022.114531_b23 article-title: A radial basis meshless method for solving inverse boundary value problems publication-title: Commun. Numer. Methods Eng. doi: 10.1002/cnm.653 |
| SSID | ssj0006914 |
| Score | 2.4231052 |
| Snippet | The problem of determining a space-dependent source term in a time fractional diffusion equation is considered from the measured data at the final time. To... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 114531 |
| SubjectTerms | Inverse source problem Landweber iteration algorithm Lipschitz continuity Meshless method Radial basis functions Time fractional diffusion equation |
| Title | Coupling RBF-based meshless method and Landweber iteration algorithm for approximating a space-dependent source term in a time fractional diffusion equation |
| URI | https://dx.doi.org/10.1016/j.cam.2022.114531 |
| Volume | 417 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9wwELYQXNpDBW1RgYLmwKmSu3nYcXKkK1ZbKBwKSNwixw8I2gcsWYlTf0l_LDNxQqlUeuCSQ-KxLM9oZuzMfB9j-7GRTuu04IlNFEejKHiOeuYii6zH9DbzGTUnn5xm4wtxdCkvV9iw74WhssrO9wef3nrr7s2g283BbV0PzqJUKWKKSJL2IEENv0IosvKvv_6UeWRFwPfGwZxG93822xovo6kZPUkIMVem8b9j07N4M1pn77pEEQ7CWjbYipu9Z29PnlBW7z-w38P5khpqr-DntxGneGRh6u6vJ-i9IFBDg55Z-IEP9JZuAQFDGVUBenI1X9TN9RQwa4UWWfyhpolxNg3oZozjPUFuA-GKH8iNQ43CQJT04BehKwKXSTwrS7p4A3cXwMM_sovR4flwzDu2BW6SRDXceqlzr5W3sZMW45a2uY0rgRuTZkZ5PCgJKYyq8KN3cVXkwprUi1zbOHO5SjfZ6mw-c58Y6MgrKZyW0htRGFERS6WrIqOiwqa62mJRv8-l6aDIiRFjUvY1ZzclqqYk1ZRBNVvsy5PIbcDh-N9g0Suv_MuYSowTL4ttv05sh70hDvpwL_OZrTaLpdvFTKWp9lpT3GNrB9-Px6ePddbqgQ |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9wwELYoPbQcqtKHoKUwh54quZuHHSfHdsVqobscWpC4RY4fELTs0iUrceKX8GOZiRPaSm0PXHJIPJblcWbG9sz3MfYxNtJpnRY8sYniuCgKnqOeucgi6zG8zXxGxcnTo2x8Ig5P5ekaG_a1MJRW2dn-YNNba929GXSzObiq68GPKFWKmCKSpN1I5E_YU4G_L9EYfL79leeRFQHgG1tzat5fbbZJXkZTNXqSEGSuTOO_O6ffHM7oJXvRRYrwJQxmk625-Su2MX2AWb1-ze6GixVV1J7B968jTg7JwqW7Pp-h-YLADQ16bmGCDzSXbgkBRBl1AXp2tljWzfklYNgKLbT4TU0dY28a0M4Yx3uG3AbCGT-QHYcahYE46cEvQ1kEDpOIVlZ08gbuZ0APf8NORvvHwzHv6Ba4SRLVcOulzr1W3sZOWnRc2uY2rgROTJoZ5XGnJKQwqsKP3sVVkQtrUi9ybePM5Sp9y9bni7nbYqAjr6RwWkpvRGFERTSVroqMigqb6mqbRf08l6bDIidKjFnZJ51dlKiaklRTBtVss08PIlcBiON_jUWvvPKP1VSio_i32LvHie2xZ-Pj6aScHBx9e8-eEyF9OKTZYevNcuU-YNjSVLvtsrwH3B_sDw |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Coupling+RBF-based+meshless+method+and+Landweber+iteration+algorithm+for+approximating+a+space-dependent+source+term+in+a+time+fractional+diffusion+equation&rft.jtitle=Journal+of+computational+and+applied+mathematics&rft.au=Salehi+Shayegan%2C+Amir+Hossein&rft.date=2023-01-01&rft.issn=0377-0427&rft.volume=417&rft.spage=114531&rft_id=info:doi/10.1016%2Fj.cam.2022.114531&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_cam_2022_114531 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0377-0427&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0377-0427&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0377-0427&client=summon |