A new numerical method for nonlinear Volterra-Fredholm
integro-differential equations
Abstract
Based on the good properties of reproducing kernel space, a new method
com bining the simplified reproducing kernel method (SRKM) and homotopy
per turbation method (HPM) for solving the nonlinear Volterra-Fredholm
integro differential equations (V-FIDE) is proposed. The HPM can convert
nonlinear problems into linear problems. And then using the SRKM to
solve linear prob lems. The uniform convergence of the approximate
solution is proved. Some numerical examples are prepared to illustrate
the efficiency and rapidity of this method.