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 CESTAC1 method for solving IEs. The accuracy of method is shown by proving a main theorem. Also, the CADNA2 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.
NSTL
Elsevier