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A Compendium of Partial Differential Equation Models
Method of Lines Analysis with Matlab

£82.00

  • Date Published: May 2009
  • availability: Available
  • format: Hardback
  • isbn: 9780521519861

£ 82.00
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  • Mathematical modelling of physical and chemical systems is used extensively throughout science, engineering, and applied mathematics. To use mathematical models, one needs solutions to the model equations; this generally requires numerical methods. This book presents numerical methods and associated computer code in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs). The authors focus on the method of lines (MOL), a well-established procedure for all major classes of PDEs, where the boundary value partial derivatives are approximated algebraically by finite differences. This reduces the PDEs to ordinary differential equations (ODEs) and makes the computer code easy to understand, implement, and modify. Also, the ODEs (via MOL) can be combined with any other ODEs that are part of the model (so that MOL naturally accommodates ODE/PDE models). This book uniquely includes a detailed line-by-line discussion of computer code related to the associated PDE model.

    • Includes line-by-line analysis and solutions for computer code associated with model equations
    • Offers a detailed presentation of ODE/PDE mathematical models
    • Methodology covers a broad spectrum of problems in science, engineering and applied mathematics
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    Reviews & endorsements

    'The presented book is very interesting not only for students in applied mathematics, physics and engineering, but also for their teachers and can act as an effective and useful motivation in their work.' Zentralblatt MATH

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    Product details

    • Date Published: May 2009
    • format: Hardback
    • isbn: 9780521519861
    • length: 490 pages
    • dimensions: 260 x 182 x 31 mm
    • weight: 1.1kg
    • contains: 58 b/w illus. 2 colour illus. 43 tables
    • availability: Available
  • Table of Contents

    1. An introduction to the Method of Lines (MOL)
    2. A one-dimensional, linear partial differential equation
    3. Green's function analysis
    4. Two nonlinear, variable coeffcient, inhomogeneous PDEs
    5. Euler, Navier-Stokes and Burgers equations
    6. The Cubic Schrödinger Equation (CSE)
    7. The Korteweg-deVries (KdV) equation
    8. The linear wave equation
    9. Maxwell's equations
    10. Elliptic PDEs: Laplace's equation
    11. Three-dimensional PDE
    12. PDE with a mixed partial derivative
    13. Simultaneous, nonlinear, 2D PDEs in cylindrical coordinates
    14. Diffusion equation in spherical coordinates
    Appendix 1: partial differential equations from conservation principles: the anisotropic diffusion equation
    Appendix 2: order conditions for finite difference approximations
    Appendix 3: analytical solution of nonlinear, traveling wave partial differential equations
    Appendix 4: implementation of time varying boundary conditions
    Appendix 5: the DSS library
    Appendix 6: animating simulation results.

  • Resources for

    A Compendium of Partial Differential Equation Models

    William E. Schiesser, Graham W. Griffiths

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  • Authors

    William E. Schiesser, Lehigh University, Pennsylvania
    William E. Schiesser is the Emeritus R. L. McCann Professor of Chemical Engineering and a Professor of Mathematics at Lehigh University. He is also a visiting professor at the University of Pennsylvania and the co-author of the Cambridge book Computational Transport Phenomena.

    Graham W. Griffiths, City University London
    Graham W. Griffiths is a visiting professor in the School of Engineering and Mathematical Sciences of City University, London, having previously been a senior visiting Fellow. He is also a founder of Special Analysis and Simulation Technology Ltd and has worked extensively in, and researched into, the field of dynamic simulation of chemical processes.

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