A First Course in Partial Differential Equations

This page links to resources supporting the textbook, A First Course in Partial Differential Equations, written by Robert Buchanan and Zhoude Shao, and published by World Scientific and Imperial College Press.

The remaining links are to Java source code files for examples and exercises from the textbook chapter on finite difference techniques for approximating solutions to partial differential equations.

• Explicit method for approximating the solution to the heat equation with homogeneous Dirichlet boundary conditions. This method is used to generate the data plotted in Figs. 12.2-12.4.
• Crank-Nicolson implicit method for approximating the solution to the heat equation with homogeneous Dirichlet boundary conditions. This method is used in Example 12.1.
• Crank-Nicolson implicit method for approximating the solution to the heat equation with homogeneous Robin boundary conditions.
• Explicit method for approximating the solution to the wave equation with homogeneous Dirichlet boundary conditions. This method is used in Example 12.2.
• Implicit method for approximating the solution to the wave equation with homogeneous Dirichlet boundary conditions. This method is used in Example 12.3.
• Jacobi iterative method for appoximating the solution to a linear system of equations. This method is used in Example 12.6.
• Gauss-Seidel iterative method for appoximating the solution to a linear system of equations. This method is used in Example 12.7.
• Use of the Gauss-Seidel iterative method to approximate the solution to Laplace's equation. This method is used to generate the data plotted in Fig. 12.10.
• A comparison of the Gauss-Seidel and Successive Over-Relaxation methods for approximating the solutions to linear systems of equations. This program is used to generate the data tabulated in Example 12.8.
• Use of the Successive Over-Relaxation method to approximate the solution to Poisson's equation. This method is used in Example 12.9.
• Solution to Exercise 08.
• Solution to Exercise 09.
• Solution to Exercise 10.
• Solution to Exercise 11.
• Solution to Exercise 12.
• Solution to Exercise 13.
• Solution to Exercise 14.
• Solution to Exercise 17.
• Solution to Exercise 18.
• Solution to Exercise 20.

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