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

Abstract

A novel numerical scheme depending on Lattice Boltzmann method is proposed to solve the Sharma–Tasso–Olver equation in one, two and three dimension. The local equilibrium distribution functions and modified functions are obtained via Taylor expansion and Chapman–Enskog multiscale expansion techniques. The macro equation is recovered accurately based on the above functions, and the stability conditions of the equations are deduced. In addition, through simulating numerically some of the initial‐boundary value problems of multidimensional STO equations, the results demonstrate that the numerical solutions and the exact solutions tend to be identical. It also indicates that the model is feasible within a specific range and provides a reliable the approach for solving the multidimensional STO equations.