Numerical solution of integrodifferential equations with convolution integrals

A numerical solution is presented for the solution of integrodifferential equations involving convolution integrals. These equations can be viewed as a generalization of the fractional differential equations, where the convolution integral represents the fractional derivative. The presented method is based on the concept of the analog equation, which converts the integrodifferential equation into a single-term ordinary differential equation, the analog equation. The latter is solved using an integral equation method. The method applies to linear and nonlinear integrodifferential equations with constant and variable coefficients as well. The resulting numerical scheme is stable, second-order accurate and simple to program on a computer. Several numerical examples with different kernels are presented, which demonstrate the efficiency and accuracy of the method showing thus the excellent performance of the numerical scheme.