Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via Tau-collocation method with convergence analysis
In this paper, we consider the nonlinear Volterra–Fredholm–Hammerstein integral equations. The approximate solution for the nonlinear Volterra–Fredholm–Hammerstein integral equations is obtained by using the Tau-Collocation method. To do this, the nonlinear Volterra–Fredholm–Hammerstein integral equ...
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| Published in | Journal of computational and applied mathematics Vol. 308; pp. 435 - 446 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
15.12.2016
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| Abstract | In this paper, we consider the nonlinear Volterra–Fredholm–Hammerstein integral equations. The approximate solution for the nonlinear Volterra–Fredholm–Hammerstein integral equations is obtained by using the Tau-Collocation method. To do this, the nonlinear Volterra–Fredholm–Hammerstein integral equations is transformed into a system of nonlinear algebraic equations in matrix form. Thus by solving this system unknown coefficients are obtained. The spectral rate of convergence for the proposed method is established in the L2-norm. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the Tau-collocation method is of high accuracy, more convenient and efficient for solving nonlinear Volterra–Fredholm–Hammerstein integral equations. |
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| AbstractList | In this paper, we consider the nonlinear Volterra–Fredholm–Hammerstein integral equations. The approximate solution for the nonlinear Volterra–Fredholm–Hammerstein integral equations is obtained by using the Tau-Collocation method. To do this, the nonlinear Volterra–Fredholm–Hammerstein integral equations is transformed into a system of nonlinear algebraic equations in matrix form. Thus by solving this system unknown coefficients are obtained. The spectral rate of convergence for the proposed method is established in the L2-norm. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the Tau-collocation method is of high accuracy, more convenient and efficient for solving nonlinear Volterra–Fredholm–Hammerstein integral equations. In this paper, we consider the nonlinear Volterra-Fredholm-Hammerstein integral equations. The approximate solution for the nonlinear Volterra-Fredholm-Hammerstein integral equations is obtained by using the Tau-Collocation method. To do this, the nonlinear Volterra-Fredholm-Hammerstein integral equations is transformed into a system of nonlinear algebraic equations in matrix form. Thus by solving this system unknown coefficients are obtained. The spectral rate of convergence for the proposed method is established in the L-norm. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the Tau-collocation method is of high accuracy, more convenient and efficient for solving nonlinear Volterra-Fredholm-Hammerstein integral equations. |
| Author | Allahviranloo, T. Gouyandeh, Z. Armand, A. |
| Author_xml | – sequence: 1 givenname: Z. orcidid: 0000-0002-8485-7436 surname: Gouyandeh fullname: Gouyandeh, Z. email: Zgouyandeh@yahoo.com organization: Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Iran – sequence: 2 givenname: T. surname: Allahviranloo fullname: Allahviranloo, T. email: Tofigh@allahviranloo.com organization: Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran – sequence: 3 givenname: A. surname: Armand fullname: Armand, A. email: Atefeh.armand@ymail.com organization: Young researchers and Elite Club, Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran |
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| Cites_doi | 10.1016/S0377-0427(99)00297-6 10.1016/S0898-1221(01)00300-5 10.1016/0022-247X(80)90297-8 10.1016/j.matcom.2005.02.035 10.1016/j.cnsns.2010.06.013 10.1016/0168-9274(92)90018-9 10.2140/pjm.1988.135.157 10.1007/s11075-009-9297-9 10.1137/0706044 10.1016/S0377-0427(02)00862-2 10.1016/j.jcp.2003.10.001 10.1016/0895-7177(88)90577-8 10.1016/j.cnsns.2011.04.023 |
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| Keywords | Nonlinear Volterra–Fredholm–Hammerstein integral equations Matrix representation Tau-collocation method Sobolev space |
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Simul. doi: 10.1016/j.cnsns.2011.04.023 contributor: fullname: Maleknejad – volume: 200 start-page: 12 year: 2007 ident: 10.1016/j.cam.2016.06.028_br000035 article-title: On an integral equation for axially symmetric problem in the case of an elastic body containing an inclusion publication-title: J. Comput. Appl. Math. contributor: fullname: Semetanian – year: 2006 ident: 10.1016/j.cam.2016.06.028_br000120 contributor: fullname: Canuto – year: 1977 ident: 10.1016/j.cam.2016.06.028_br000015 contributor: fullname: Jaswon – year: 2004 ident: 10.1016/j.cam.2016.06.028_br000100 contributor: fullname: Chi Ngai |
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| Snippet | In this paper, we consider the nonlinear Volterra–Fredholm–Hammerstein integral equations. The approximate solution for the nonlinear... In this paper, we consider the nonlinear Volterra-Fredholm-Hammerstein integral equations. The approximate solution for the nonlinear... |
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| SubjectTerms | Approximation Computation Convergence Integral equations Mathematical analysis Mathematical models Matrix representation Nonlinear Volterra–Fredholm–Hammerstein integral equations Nonlinearity Sobolev space Spectra Tau-collocation method |
| Title | Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via Tau-collocation method with convergence analysis |
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