A meshless algorithm with the improved moving least square approximation for nonlinear improved Boussinesq equation

An improved moving least square meshless method is developed for the numerical solution of the nonlinear improved Boussinesq equation. After the approximation of temporal derivatives, nonlinear systems of discrete algebraic equations are established and are solved by an iterative algorithm. Convergence of the iterative algorithm is discussed. Shifted and scaled basis functions are incorporated into the method to guarantee convergence and stability of numerical results. Numerical examples are presented to demonstrate the high convergence rate and high computational accuracy of the method.

Automated summary

An improved moving least square meshless method is developed for solving the numerical nonlinear improved Boussinesq equation. Nonlinear systems of discrete algebraic equations are solved using an iterative algorithm, and shifted and scaled basis functions are incorporated to ensure convergence and stability. Numerical examples demonstrate high convergence rate and computational accuracy of the method.