# 求偏微分方程的数值解（有限差分法、配置法、Galerkin方法）

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：

http://wap.sciencenet.cn/blog-516836-1292219.html

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