The Numerical Validation of the Adomian Decomposition Method for Solving Volterra Integral Equation with Discontinuous Kernels Using the CESTAC Method

The aim of this paper is to present a new method and the tool validate numerical results Volterra integral equation with discontinuous kernels in linear non-linear forms obtained from Adomian decomposition method. Because disadvantages traditional absolute error show accuracy mathematical methods which based on floating point arithmetic, we apply stochastic arithmetic condition study efficiency two successive approximations. Thus CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) CADNA (Control Accuracy Debugging for Numerical Applications) library are employed. Finding optimal iteration method, approximation some advantages comparison usual packages. theorems proved convergence analysis solving mentioned problem. Also, main theorem presented shows equality between number common significant digits exact approximate solutions approximations.This makes possible termination criterion instead error. Several examples both nonlinear cases solved floating-point compared demonstrate novel