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

作　　者：K.Maleknejad M.Soleiman Dehkordi 

机构地区：[1]School of Mathematics,Iran University of Science and Technology,Narmak,Tehran 16844,Iran.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2021年第1期83-98,共16页高校应用数学学报（英文版）（B辑）

摘　　要：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.

关 键 词：he two-dimensional nonlinear integral equations the nonlinear mixed Volterra-Fredholm inte-gral equations two-dimensional Laguerre wavelet Orthogonal polynomial convergence analysis the Darboux problem. 

分 类 号：O241.83[理学—计算数学]