Solving second order two-point boundary value problems accurately by a third derivative hybrid block integrator
•A hybrid block integrator for solving second order two-point boundary value problems is presented.•A theoretical analysis of the method has been done.•Some numerical experiments have been presented in order to illustrate good performance of the integrator. This article deals with the development of...
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| Published in | Applied mathematics and computation Vol. 421; p. 126960 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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15.05.2022
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| Abstract | •A hybrid block integrator for solving second order two-point boundary value problems is presented.•A theoretical analysis of the method has been done.•Some numerical experiments have been presented in order to illustrate good performance of the integrator.
This article deals with the development of an optimized third-derivative hybrid block method for integrating general second order two-point boundary value problems (BVPs) subject to different types of boundary conditions (BCs) such as Dirichlet, Neumann or Robin. A purely interpolation and collocation approach has been used in order to develop the method. A constructive approach has been applied in the development of the method to consider two off-step optimal points among an infinite number of possible choices in a two-step block corresponding to a generic interval of the form [xn,xn+2]. The obtained method simultaneously produces an approximate solution over the entire integration interval. Some numerical experiments have been presented that show the good performance of the presented scheme. |
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| AbstractList | •A hybrid block integrator for solving second order two-point boundary value problems is presented.•A theoretical analysis of the method has been done.•Some numerical experiments have been presented in order to illustrate good performance of the integrator.
This article deals with the development of an optimized third-derivative hybrid block method for integrating general second order two-point boundary value problems (BVPs) subject to different types of boundary conditions (BCs) such as Dirichlet, Neumann or Robin. A purely interpolation and collocation approach has been used in order to develop the method. A constructive approach has been applied in the development of the method to consider two off-step optimal points among an infinite number of possible choices in a two-step block corresponding to a generic interval of the form [xn,xn+2]. The obtained method simultaneously produces an approximate solution over the entire integration interval. Some numerical experiments have been presented that show the good performance of the presented scheme. |
| ArticleNumber | 126960 |
| Author | Singh, Gurjinder Ramos, Higinio |
| Author_xml | – sequence: 1 givenname: Higinio surname: Ramos fullname: Ramos, Higinio email: higra@usal.es organization: Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced 37008 Salamanca, Spain – sequence: 2 givenname: Gurjinder surname: Singh fullname: Singh, Gurjinder email: gurjinder@ptu.ac.in organization: Department of Mathematical Sciences, I. K. Gujral Punjab Technical University, Jalandhar, Main Campus, Kapurthala 144603, Punjab, India |
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| Cites_doi | 10.1016/j.apm.2013.03.054 10.1090/S0025-5718-1979-0521281-7 10.1016/j.camwa.2008.09.033 10.1145/2427023.2427032 10.1007/BF01932148 10.1016/j.amc.2017.04.020 10.1016/j.amc.2014.08.046 10.1080/00207169108804026 10.1007/s11075-019-00753-3 10.1145/355945.355950 10.1093/imamat/22.2.203 10.1007/s11075-015-0081-8 10.1016/0045-7825(83)90075-0 10.3846/mma.2021.12940 10.1016/j.matcom.2019.03.003 10.1016/j.cam.2015.12.018 10.1016/j.apnum.2008.03.036 10.1080/00207160601025656 10.1155/2014/379829 10.1063/1.4912313 10.1016/j.cam.2020.112876 10.1016/S0377-0427(99)00093-X 10.7494/OpMath.2014.34.2.387 10.1016/j.cam.2021.113419 10.1016/j.amc.2018.03.098 10.1016/S0898-1221(98)80028-X 10.1016/j.mcm.2010.06.023 10.1016/j.aml.2016.08.012 10.1007/BF01932284 10.1016/j.amc.2007.02.027 10.1007/978-90-481-9981-5_2 10.1016/j.cam.2012.04.011 10.1007/BF01933410 10.1016/S0898-1221(01)00250-4 10.1016/j.cpc.2011.12.017 10.1090/S0025-5718-1969-0264854-5 10.1016/j.cam.2004.07.008 10.1016/0168-9274(95)00045-V 10.1016/S0893-9659(02)00039-3 10.1016/j.camwa.2006.12.060 |
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| Snippet | •A hybrid block integrator for solving second order two-point boundary value problems is presented.•A theoretical analysis of the method has been done.•Some... |
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| SubjectTerms | Block scheme Boundary value problems Convergence Optimization strategy Ordinary differential equations |
| Title | Solving second order two-point boundary value problems accurately by a third derivative hybrid block integrator |
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