5 Exercises

• 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.