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

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.

Automated summary

An efficient scheme is presented in this research to validate numerical results and solve second kind integral equations. By using the homotopy perturbation method and stochastic arithmetic, the method can achieve optimal approximation, iteration, validation of results, and handle numerical instability. The importance of applying stochastic arithmetic is demonstrated through solving examples.