Table of Contents

1. Partial Differential Equation Applications.- 1.1 Energy Minimization.- 1.2 Mass Balance.- 1.3 Force Balance.- 1.4 Resonance.- 1.5 PDE/PROTRAN.- 1.6 Exercises.- 2. Elliptic Problems—Forming the Algebraic Equations.- 2.1 The Galerkin Method.- 2.2 Lagrangian Isoparametric Triangular Elements.- 2.3 Numerical Integration.- 2.4 Triangulation Refinement and Grading.- 2.5 Exercises.- 3. Elliptic Problems—Solving the Algebraic Equations.- 3.1 The Newton-Raphson Method.- 3.2 The Band Solver.- 3.3 The Frontal Solver.- 3.4 The Lanczos Solver.- 3.5 Exercises.- 4. Parabolic Problems.- 4.1 The Time Discretization.- 4.2 Stability.- 4.3 Solving the Linear Equations.- 4.4 Exercises.- 5. Hyperbolic problems.- 5.1 First Order Transport Problems.- 5.2 Second Order Wave Problems.- 5.3 Exercises.- 6. Eigenvalue Problems.- 6.1 The Rayleigh-Ritz Approximation.- 6.2 The Inverse Power Method.- 6.3 Exercises.- Appendices.- 1. Lanczos Iteration Properties.- 2. The PROTRAN Preprocessor.- 3. PDE/PROTRAN Keywords.- 4. Postscript.