- Exercise 1: An alternate form of the equation for conservation of material.
- Exercise 2: Inclusion of a source/sink term in the original form of the material conservation equation.
- Exercise 3: Inclusion of a source/sink term in the alternate form of the material conservation equation.
- Exercise 4: Derivation of difference quotient formulas using Taylor's Theorem.
- Exercise 5: An evaluation of the error in the computer implementation of the centered difference formula.
- Exercise 6: An illustration of the error analysis of the previous exercise.
- Exercise 7: The Crank--Nicolson Finite Difference Equation.
- Exercise 8: Derivation of the diffusion-convection conservation law PDE.
- Exercise 9: Derivation of FDEs for various forms of sigma and v.
- Exercise 10: Repeat Exercise 9 deriving FDEs that are implicit, backward in time.
- Exercise 11: A computer program to solve a set of FDEs.
- Exercise 12: Explicit FDE used to approximate the solution to an IBVP.
- Exercise 13: Implicit FDE used to approximate the solution to an IBVP.
- Exercise 14: A computer program to factor a tridiagonal matrix.
- Exercise 15: Approximate the solution to a centered difference FDE.
- Exercise 16: IBVP solution approximated by an implicit FDE with centered difference.
- Exercise 17: IBVP solution approximated by an explicit FDE.
- Exercise 18: Solution to another IBVP approximated by an explicit FDE.
- Exercise 19: Graph of a solution of Exercise 18.
- Exercise 20: Use PlotMTV to display the results of Exercise 18 as a raster map.
- Exercise 21: Prescribing the U-values of one or more FDE cells.
- Exercise 22: The computational technique known as "blasting".
- Exercise 23: An illustration of blasting.
- Exercise 24: Repeat Exercise 23 using the implicit, backward in time method.
- Exercise 25: An illustration of a "no-flow cell".
- Exercise 26: An examination of heat flow.
- Exercise 27: Develop the backward in time FDE for an PDE.
- Exercise 28: Develop the Crank--Nicolson FDE for a PDE.
- Exercise 29: Approximate solution to an IBVP and display of the solution.
- Exercise 30: A formulation of a system of finite difference equations using the explicit method.
- Exercise 31: Developing a system of FDEs for an elliptic BVP.
- Exercise 32: Write a system of FDEs for a heat flow problem, solve the system, and display the results.
- Exercise 33: Rework Exercise 32 with the assumption that the L-shaped shaded region has conductivity sigma=1 and is held at temperature 100 degrees.