Efficient Numerical Solution of the Sharma-Tasso-Olver Equation Using Radial Basis Function-Pseudo Spectral Method with Comparative Analysis

Abstract

In this study, we will solve the Sharma-Tasso-Olver equation by utilizing the radial basis function-pseudo spectral approach. Pseudo spectral techniques are renowned for their exceptional precision but have constraints regarding their ability to handle geometric variations. The integration of Radial Basis Functions (RBF) with pseudo spectral methods offers a solution to surmount this particular limitation. To estimate the differentials with respect to the variable , we will use the radial basis functions, including commonly used ones like multiquadric, inverse multiquadric, and inverse quadric, have been employed. Furthermore, the problem has transformed into the ordinary differential equation (ODE), and the solution to this ODE system has been acquired through the application of the fourth-order Runge-Kutta method. Additionally, a comparative analysis has been conducted between the solutions obtained through the suggested technique and the exact solutions.