Numerical solution of nonlinear integral equations using alternative Legendre polynomials |
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| Authors: | Sohrab Bazm Alireza Hosseini |
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| Affiliation: | 1.Department of Mathematics, Faculty of Science,University of Maragheh,Maragheh,Iran;2.School of Mathematics, Statistics and Computer Science, College of Science,University of Tehran,Tehran,Iran;3.School of Mathematics, Institute for Research in Fundamental Sciences (IPM),Tehran,Iran |
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| Abstract: | In this paper, the operational matrices of integration and the product for the alternative Legendre polynomials (ALPs) are first derived. Then, using these operational matrices and the collocation method, the nonlinear Volterra–Fredholm–Hammerstein integral equations are reduced to a set of nonlinear algebraic equations with unknown ALP coefficients. Some error estimations are provided and the efficiency and accuracy is verified by applying the method to some examples chosen from other literature. |
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