Numerical solutions of two-dimensional nonlinear integral equations via Laguerre Wavelet method with convergence analysis
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：
the two-dimensional nonlinear integral equations,
the nonlinear mixed Volterra-Fredholm integral equations,
two-dimensional Laguerre wavelet,
Orthogonal polynomial,
convergence analysis,
the Darboux problem
