[eBook Code] Solving Partial Differential Equation Applications with PDE2D (eBook Code, 1st)

Preface vii

I Introduction to PDE2D 1

I.1 The Collocation and Galerkin Finite Element Methods 1

I.2 The PDE2D User Interfaces 7

I.3 Accuracy 11

I.4 Computer Time and Memory 13

I.5 Programming Hints 17

1 The Damped Spring and Pendulum Problems 21

1.1 Derivation of the Damped Spring and Pendulum Equations 21

1.2 Damped Spring and Pendulum Examples 23

1.3 Problems 24

2 Beam and Plate Bending 31

2.1 Derivation of Beam Bending Equation 31

2.2 Derivation of Plate Bending Equation 32

2.3 Beam and Plate Examples 33

2.4 Problems 34

3 Diffusion and Heat Conduction 39

3.1 Derivation of Diffusion Equation 39

3.2 Diffusion and Heat Conduction Examples 40

3.3 Problems 51

4 Pricing Options 61

4.1 Derivation of Black–Scholes Equation 61

4.2 Option Pricing Examples 65

4.3 Problems 70

5 Elasticity 75

5.1 Derivation of Elasticity Equations 75

5.2 Elasticity Examples 77

5.3 Problems 81

6 Incompressible Fluid Flow 95

6.1 Derivation of Navier–Stokes Equations 95

6.2 Stream Function and PenaltyMethod Approaches 97

6.3 Fluid Flow Examples 97

6.4 Problems 105

7 The Schrödinger and Other Eigenvalue Equations 119

7.1 The Schrödinger Equation 119

7.2 Schrödinger and Maxwell Equations Examples 119

7.3 Problems 126

8 Minimal Surface and MembraneWave Equations 137

8.1 Derivation of Minimal Surface Equation 137

8.2 Derivation of MembraneWave Equation 138

8.3 Examples 140

8.4 Problems 142

9 The KPIWave Equation 149

9.1 A Difficult Nonlinear Problem 149

9.2 Numerical Results 155

Appendix A: Formulas from Multivariate Calculus 161

Appendix B: Algorithms Used by PDE2D 163

Appendix C: Equations Solved by PDE2D 183

Appendix D: Problem 5.7 Local Solvers 193

References 205

Index 207