The Petrov–Galerkin finite element method for the numerical solution of time-fractional Sharma–Tasso–Olver equation

Abstract

In this paper, time-fractional Sharma–Tasso–Olver (STO) equation has been solved numerically through the Petrov–Galerkin approach utilizing a quintic B-spline function as the test function and a linear hat function as the trial function. The Petrov–Galerkin technique is effectively implemented to the fractional STO equation for acquiring the approximate solution numerically. The numerical outcomes are observed in adequate compatibility with those obtained from variational iteration method (VIM) and exact solutions. For fractional order, the numerical outcomes of fractional Sharma–Tasso–Olver equations are also compared with those obtained by variational iteration method (VIM) in Song et al. [Song L., Wang Q., Zhang H., Rational approximation solution of the fractional Sharma–Tasso–Olver equation, J. Comput. Appl. Math. 224:210–218, 2009]. Numerical experiments exhibit the accuracy and efficiency of the approach in order to solve nonlinear fractional STO equation.

Numerical solutions to the Sharma–Tasso–Olver equation using Lattice Boltzmann method

“…Referring to the relevant literature, 6,13,14 it can be found that the process of solving the exact solution of the STO equation is complex, and the application flexibility of these methods is poor. In addition, traditional numerical solution methods, such as the finite difference (FD) method 16 and the finite element (FE) method 17 also be considered to study the kind of equation. However, traditional methods are difficult to handle complex boundary conditions, and their iterative format is sophisticated.…”