Solving Partial Differential Equation Applications with PDE2D

Inbunden, Engelska, 2018

Av Granville Sewell, Granville (University of Texas at El Paso) Sewell

1 449 kr

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Solve engineering and scientific partial differential equation applications using the PDE2D software developed by the author Solving Partial Differential Equation Applications with PDE2D derives and solves a range of ordinary and partial differential equation (PDE) applications. This book describes an easy-to-use, general purpose, and time-tested PDE solver developed by the author that can be applied to a wide variety of science and engineering problems. The equations studied include many time-dependent, steady-state and eigenvalue applications such as diffusion, heat conduction and convection, image processing, math finance, fluid flow, and elasticity and quantum mechanics, in one, two, and three space dimensions.The author begins with some simple "0D" problems that give the reader an opportunity to become familiar with PDE2D before proceeding to more difficult problems. The book ends with the solution of a very difficult nonlinear problem, which requires a moving adaptive grid because the solution has sharp, moving peaks. This important book: Describes a finite-element program, PDE2D, developed by the author over the course of 40 yearsDerives the ordinary and partial differential equations, with appropriate initial and boundary conditions, for a wide variety of applicationsOffers free access to the Windows version of the PDE2D software through the author’s website at www.pde2d.comOffers free access to the Linux and MacOSX versions of the PDE2D software also, for instructors who adopt the book for their course and contact the author at www.pde2d.comWritten for graduate applied mathematics or computational science classes, Solving Partial Differential Equation Applications with PDE2D offers students the opportunity to actually solve interesting engineering and scientific applications using the accessible PDE2D.

Produktinformation

Utgivningsdatum2018-12-07
Mått152 x 231 x 18 mm
Vikt499 g
FormatInbunden
SpråkEngelska
Antal sidor224
FörlagJohn Wiley & Sons Inc
ISBN9781119507932

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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