Maple worksheets on finite difference methods
Numerical methods topics:
- Introduction - errors
- 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 TridiagSolve to 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
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