Maple worksheets on finite difference methods |

Numerical methods topics:

- Introduction - errors
- Root-finding
- Interpolation
- Numerical integration
- 1st order differential equations
- 2nd order differential equations
- Linear systems
- Finite difference methods
- The Duffing equation
- Approximation of functions
- The numerical evaluation of mathematical functions
- Special inverse functions
- The derivation of Runge-Kutta schemes
- Interpolation for Runge-Kutta schemes

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

Numerical differentiation- numdiff.mws

- Simple formulas for computing numerical approximations for 1st and 2nd derivatives of a tabulated function.
- Improving the accuracy of numerical differentiation by extrapolation.
- Constructing extrapolation formulas.

Two point boundary value problems- FDintro.mws

- The finite difference method for constructing a discrete numerical solution for a two point boundary value problem.
- An example using standard method to solve the tridiagonal system which arises when applying the finite difference method to solve a two point boundary value problem.
- Using the procedure
TridiagSolveto solve the tridiagonal system arising from a two point boundary value problem.

Discrete and continuous numerical solutions for boundary value problems- desolveFD.mws

- A procedure for constructing both discrete and continuous solutions to boundary value problems:
desolveFD.

The continuous solutions are constructed by means of local Taylor series approximations.

Boundary value examples involving special functions- FDspec.mws

- Examples of boundary value problems where the analytical solution involves special functions such as a Bessel functions, Legendre polynomials, etc.

Procedures for differential equations- DEsol.zip