3. Fundamentals and Solution of Differential Equations

  1. Dr. Dierk Raabe1,2

Published Online: 24 MAR 2004

DOI: 10.1002/3527601945.ch3

Computational Materials Science: The Simulation of Materials, Microstructures and Properties

Computational Materials Science: The Simulation of Materials, Microstructures and Properties

How to Cite

Raabe, D. (1998) Fundamentals and Solution of Differential Equations, in Computational Materials Science: The Simulation of Materials, Microstructures and Properties, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527601945.ch3

Author Information

  1. 1

    Department for Materials Science & Engineering, Carnegie Mellon University, Room 3317, Wean Hall, Pittsburgh, PA 15213-3890, USA

  2. 2

    Institut für Metallkunde und Metallphysik, RWTH Aachen, Kopernikusstraße 14, 52056 Aachen, Germany

Publication History

  1. Published Online: 24 MAR 2004
  2. Published Print: 1 JUN 1998

ISBN Information

Print ISBN: 9783527295418

Online ISBN: 9783527601943

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Keywords:

  • differential equations;
  • solution;
  • finite difference method;
  • Euler methods;
  • Leap-Frog method;
  • predictor–corrector methods;
  • Crank–Nicholson method;
  • Runge–Kutta methods;
  • Ritz variational method

Summary

This chapter contains sections titled:

  • Introduction to Differential Equations

  • Solution of Partial Differential Equations

  • Fundamentals of the Finite Difference Method

    • Discretization of Time

    • Numerical Errors of Finite Difference Methods

    • Euler Methods

    • Leap-Frog Method

    • Predictor–Corrector Methods

    • Crank–Nicholson Method

    • Runge–Kutta Methods

  • Fundamentals of the Finite Element Method

    • Discretization and Basic Procedure

    • The Ritz Variational Method