# Numerical solutions of two-dimensional nonlinear integral equations via Laguerre Wavelet method with convergence analysis

Numerical solutions of two-dimensional nonlinear integral equations via Laguerre Wavelet method... In this paper, the approximate solutions for two different type of two-dimensional nonlinear integral equations: two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method. To do this, these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form. By solving these systems, unknown coefficients are obtained. Also, some theorems are proved for convergence analysis. Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics-A Journal of Chinese Universities Springer Journals

# Numerical solutions of two-dimensional nonlinear integral equations via Laguerre Wavelet method with convergence analysis

, Volume 36 (1) – Mar 10, 2021
16 pages      /lp/springer-journals/numerical-solutions-of-two-dimensional-nonlinear-integral-equations-HMg0h4O5LK
Publisher
Springer Journals
ISSN
1005-1031
eISSN
1993-0445
DOI
10.1007/s11766-021-3656-2
Publisher site
See Article on Publisher Site

### Abstract

In this paper, the approximate solutions for two different type of two-dimensional nonlinear integral equations: two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method. To do this, these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form. By solving these systems, unknown coefficients are obtained. Also, some theorems are proved for convergence analysis. Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.

### Journal

Applied Mathematics-A Journal of Chinese UniversitiesSpringer Journals

Published: Mar 10, 2021