偏微分方程PDE通常用于描述各种各样的现象，例如声、热、电、电动力学、弹性力学、流体力学等。

计算环境：Maple 2015 - Maple 2021 下载Maple计算文件 Finite difference method approximate differential equations using finite difference equations to approximate derivatives

Collocation method uses a finite-dimensional space of basis functions and collocation points to approximate PDEs

Galerkin’s technique uses orthogonality of a set of basis function to turn PDEs into coupled sets of ODEs

Finite difference method The derivatives of the PDE are approximated by linear combinations of function values at the structured grid points, using a Taylor series expansion Collocation method Define the basis function (usually polynomials) and approximate solution: Calculate residual function by substituting the candidate function into the original PDE Choose the collocation points at which the candidate function must exactly match Galerkin’s method

Define the basis function (usually orthogonal polynomials) and approximate solution as Calculate residual function by substituting the candidate function into the original PDE Minimize the residual using Least Squares Error Maple中的计算文件： 基于PDE的应用示例： 电池数学模型白皮书