The combined reproducing kernel method and Taylor series for handling nonlinear Volterra integro-differential equations with derivative type kernel

摘要

The reproducing kernel method is applied to Volterra nonlinear integro-differential equations. In this technique, the nonlinear term is replaced by its Taylor series. The exact solution is represented in the form of series in the reproducing Hilbert kernel space. The approximation solution is expressed by n-term summation of reproducing kernel functions. Some numerical examples are solved in two different spaces and parameters of n. Measurements of the experimental data is an indications of stability and convergence on the reproducing kernel.