Dynamical strategy on homotopy perturbation method for solving second kind integral equations using the CESTAC method

Abstract

In this research, an efficient scheme is presented to validate the numerical results and solve the second kind integral equations (IEs). For this reason the homotopy perturbation method (HPM) is illustrated and the stochastic arithmetic is applied to implement the CESTAC11Controle et Estimation Stochastique des Arrondis de Calculs. method for solving IEs. The accuracy of method is shown by proving a main theorem. Also, the CADNA22Control of Accuracy and Debugging for Numerical Applications. library is used instead of other usual softwares. Applying the mentioned method, the optimal approximation, iteration, validation of results and any numerical instability can be found whereas the floating-point arithmetic (FPA) has not these properties. Some examples are solved to determine the significance of applying the SA in place of the FPA.