非线性Gilson-Pickering方程的移动最小二乘近似无网格法

Analysis of Nonlinear Gilson-Pickering Equation by Moving Least Square Approximate Meshless Method

【目的】利用适定移动最小二乘近似和预测校正迭代算法等技术,建立数值分析Gilson-Pickering方程的移动最小二乘近似无网格方法。【方法】首先采用差分格式离散时间导数,然后利用适定移动最小二乘近似离散空间导数,最后使用配点技术得到了非线性代数方程组。【结果】数值算例表明该方法能有效地求解具有三阶偏导数且依赖于时间变量的非线性Gilson-Pickering方程。【结论】该方法比有限元方法的精度更高。

[Purposes]Using the well-posed moving least squares approximation and the predictor-corrector iterative algorithm, a meshless method is established for numerical analysis of the Gilson-Pickering equation using moving least squares approximation. [Methods] The difference formulas are used to discretize the time derivatives, the well-defined moving least squares approximation is used to discrete the space derivatives, and finally the collocation technique is used to obtain the nonlinear algebraic equations. [Findings] Numerical examples show that the method can effectively solve the nonlinear Gilson-Pickering equation with third-order partial derivatives and time-dependent variables. [Conclusions] This method is more accurate than the finite element method.