Table of Contents

1. Basic Routines

• Machine Epsilon
• Absolute Error
• Relative Error
• First Order Initial Value Problem
• Logistic Differencial Equations
• Second Order, Linear, Constant Coefficient, DEQ
• Finite Difference Coefficients
• Gaussian Elimination

2. Elliptic Problems

• Thomas Algorithm
• LU Factorization
• Jacobi Iteration
• Initializing an Elliptic DE
• Matrix One Norm
• Matrix Infinity Norm
• Power Method
• Inverse Power Method
• 5 Point Stencil
• 9 Point Stencil
• Gauss-Seidel Method
• Conjugate Gradient Method
• Explicit Euler Method
• Explicit Euler Method Mulitiple Output
• Implicit Euler Method
• Runge Kutta 2nd Order Method
• Runge Kutta 4th Order Method
• Predictor Correcting Method

3. Routines for Parabolic Problems

• Explicit Euler PDE
• Implicit Euler PDE

4. Routines for Hyperbolic Problems

• Upwinding
• Lax-Wendroff
• Warming and Beam

5. Test Problems

• HW2 Prob.7
• HW2 Prob.9

6. Appendix

• 1-Norm
• 2-Norm
• Infinity-Norm

7. Appendix B

• Matrix Class
• Split into L D U