 徐俊林 2021-6-22 12:09 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：                            Whitepaper-Developing_Mathematical_Models_of_Batteries.pdf