Lecture notes on finite difference method pdf

1. What is the meaning of finite difference method?
2. What is difference between FEM and FDM?
3. What is the stability of finite difference method?
4. What is the difference between finite difference and finite-element method?

What is the meaning of finite difference method?

The finite difference method (FDM) is an approximate method for solving partial differential equations. It has been used to solve a wide range of problems. These include linear and non-linear, time independent and dependent problems.

What is difference between FEM and FDM?

The major differences of FDM from FEM are (1) Governing partial differential equations are approximated directly by finite difference approximation, not by interpolation functions nor via the Galerkin method, (2) The discretized whole domain is not covered by a finite number of interpolation functions, but is ...

What is the stability of finite difference method?

A finite difference scheme is stable if the errors made at one time step of the calculation do not cause the errors to be magnified as the computations are continued. A neutrally stable scheme is one in which errors remain constant as the computations are carried forward.

What is the difference between finite difference and finite-element method?

The finite-element method starts with a variational statement of the problem and introduces piecewise definitions of the functions defined by a set of mesh point values. The finite-difference method starts with a differential statement of the problem and proceeds to replace the derivatives with their discrete analogs.