Regularization technique and numerical analysis of the mixed system of first and second-kind Volterra–Fredholm integral equations
It is important to note that mixed systems of first and second-kind Volterra–Fredholm integral equations are ill-posed problems, so that solving discretized system of such problems has a lot of difficulties. We will apply the regularization method to convert this mixed system (ill-posed problem)...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2019-03-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_24823_c56ff6c60d32ee8cc0c6bc4a8604afa5.pdf |
| Summary: | It is important to note that mixed systems of first and second-kind Volterra–Fredholm integral equations are ill-posed problems, so that solving discretized system of such problems has a lot of difficulties. We will apply the regularization method to convert this mixed system (ill-posed problem) to system of the second kind Volterra–Fredholm integral equations (well-posed problem). A numerical method based on Chebyshev wavelets is suggested for solving the obtained well-posed problem, and convergence analysis of the method is discussed. For showing efficiency of the method, some test problems, for which the exact solution is known, are considered. |
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| ISSN: | 2423-6977 2423-6969 |