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

计算文件下载：

pde_approximation.zip

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：

Whitepaper-Developing_Mathematical_Models_of_Batteries.pdf