Granville Sewell, PhD, is Professor in the Mathematics department at the University of Texas-El Paso, El Paso, TX. Dr. Sewell is the author of The Numerical Solution of Ordinary and Partial Differential Equations, Second Edition, and Computational Methods of Linear Algebra, Second Edition, both published by Wiley.

Select Guide Rating

• Preface viiI Introduction to PDE2D 1I.1 The Collocation and Galerkin Finite Element Methods 1I.2 The PDE2D User Interfaces 7I.3 Accuracy 11I.4 Computer Time and Memory 13I.5 Programming Hints 171 The Damped Spring and Pendulum Problems 211.1 Derivation of the Damped Spring and Pendulum Equations 211.2 Damped Spring and Pendulum Examples 231.3 Problems 242 Beam and Plate Bending 312.1 Derivation of Beam Bending Equation 312.2 Derivation of Plate Bending Equation 322.3 Beam and Plate Examples 332.4 Problems 343 Diffusion and Heat Conduction 393.1 Derivation of Diffusion Equation 393.2 Diffusion and Heat Conduction Examples 403.3 Problems 514 Pricing Options 614.1 Derivation of Black–Scholes Equation 614.2 Option Pricing Examples 654.3 Problems 705 Elasticity 755.1 Derivation of Elasticity Equations 755.2 Elasticity Examples 775.3 Problems 816 Incompressible Fluid Flow 956.1 Derivation of Navier–Stokes Equations 956.2 Stream Function and PenaltyMethod Approaches 976.3 Fluid Flow Examples 976.4 Problems 1057 The Schrödinger and Other Eigenvalue Equations 1197.1 The Schrödinger Equation 1197.2 Schrödinger and Maxwell Equations Examples 1197.3 Problems 1268 Minimal Surface and MembraneWave Equations 1378.1 Derivation of Minimal Surface Equation 1378.2 Derivation of MembraneWave Equation 1388.3 Examples 1408.4 Problems 1429 The KPIWave Equation 1499.1 A Difficult Nonlinear Problem 1499.2 Numerical Results 155Appendix A: Formulas from Multivariate Calculus 161Appendix B: Algorithms Used by PDE2D 163Appendix C: Equations Solved by PDE2D 183Appendix D: Problem 5.7 Local Solvers 193References 205Index 207

Granville Sewell, PhD, is Professor in the Mathematics department at the University of Texas-El Paso, El Paso, TX. Dr. Sewell is the author of The Numerical Solution of Ordinary and Partial Differential Equations, Second Edition, and Computational Methods of Linear Algebra, Second Edition, both published by Wiley.

Select Guide Rating

• Preface viiI Introduction to PDE2D 1I.1 The Collocation and Galerkin Finite Element Methods 1I.2 The PDE2D User Interfaces 7I.3 Accuracy 11I.4 Computer Time and Memory 13I.5 Programming Hints 171 The Damped Spring and Pendulum Problems 211.1 Derivation of the Damped Spring and Pendulum Equations 211.2 Damped Spring and Pendulum Examples 231.3 Problems 242 Beam and Plate Bending 312.1 Derivation of Beam Bending Equation 312.2 Derivation of Plate Bending Equation 322.3 Beam and Plate Examples 332.4 Problems 343 Diffusion and Heat Conduction 393.1 Derivation of Diffusion Equation 393.2 Diffusion and Heat Conduction Examples 403.3 Problems 514 Pricing Options 614.1 Derivation of Black–Scholes Equation 614.2 Option Pricing Examples 654.3 Problems 705 Elasticity 755.1 Derivation of Elasticity Equations 755.2 Elasticity Examples 775.3 Problems 816 Incompressible Fluid Flow 956.1 Derivation of Navier–Stokes Equations 956.2 Stream Function and PenaltyMethod Approaches 976.3 Fluid Flow Examples 976.4 Problems 1057 The Schrödinger and Other Eigenvalue Equations 1197.1 The Schrödinger Equation 1197.2 Schrödinger and Maxwell Equations Examples 1197.3 Problems 1268 Minimal Surface and MembraneWave Equations 1378.1 Derivation of Minimal Surface Equation 1378.2 Derivation of MembraneWave Equation 1388.3 Examples 1408.4 Problems 1429 The KPIWave Equation 1499.1 A Difficult Nonlinear Problem 1499.2 Numerical Results 155Appendix A: Formulas from Multivariate Calculus 161Appendix B: Algorithms Used by PDE2D 163Appendix C: Equations Solved by PDE2D 183Appendix D: Problem 5.7 Local Solvers 193References 205Index 207