The Nyström Method and Convergence Analysis for System of Fredholm Integral Equations

Year 2019, Volume: 2 Issue: 1, 28 - 32, 17.06.2019

Huimin Zhou Qisheng Wang

https://doi.org/10.33401/fujma.486878

Cited By: 1

Abstract

In this paper, the efficient numerical solutions of a class of system of Fredholm integral equations are solved by the Nyström method, which discretizes the system of integral equations into solving a linear system. The existence and uniqueness of the exact solutions are proved by the Banach fixed point theorem. The format of the Nyström solutions is given, especially with the composite Trapezoidal and Simpson rules. The results of error estimation and convergence analysis are obtained in the infinite norm sense. The validity and reliability of the theoretical analysis are verified by numerical experiments.

Keywords

Convergence analysis, Error estimation, System of Fredholm integral equations

References

• [1] K. Y. Wang, Q. S. Wang, Taylor collocation method and convergence analysis for the Volterra-Fredholm integral equations, J. Comput. Appl. Math., 260 (2014), 294-300.
• [2] Q. S. Wang, K. Y. Wang, S. J. Chen, Least squares approximation method for the solution of Volterra-Fredholm integral equations, J. Comput. Appl. Math., 272 (2014), 141-147.
• [3] K. Y. Wang, Q. S. Wang, K. Z. Guan, Iterative method and convergence analysis for a kind of mixed nonlinear Volterra-Fredholm integral equation, Appl. Math. Comput., 225 (2013), 631-637.
• [4] K. Atkinson, W. Han, Theoretical Numerical Analysis: A Functional Analysis Framework (Third Edition), Springer, 2009.
• [5] X. C. Zhong, A new Nyström-type method for Fredholm integral equations of the second kind, Appl. Math. Comput., 219 (2013), 8842-8847.
• [6] L. J. Lardy, A Variation of Nyström’s Method for Hammerstein Equations, J. Integral. Equ., 3(1) (1981), 43-60.
• [7] J. Dick, P. Kritzer, F. Y. Kuo, I. H. Sloan, Lattice-Nystr¨om method for Fredholm integral equations of the second kind with convolution type kernels, J. Complexity., 23 (2007), 752-772.
• [8] Q. S. Wang, H. S. Wang, Meshless method and convergence analysis for 2-dimensional Fredholm integral equation with complex factors, J. Comput. Appl. Math., 304 (2016), 18-25.
• [9] Z. Y. Chen, C. A. Micchelli, Y. S. Xu, Multiscale Methods for Fredholm Integral Equations, Cambridge University Press, 2015.