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Numerical Approximation of Model Partial Differential Equations

In: An Introduction to Scientific Computing

Author

Listed:
  • Ionut Danaila

    (Laboratoire de Mathématiques Raphaël Salem)

  • Pascal Joly

    (Laboratoire Jacques-Louis Lions)

  • Sidi Mahmoud Kaber

    (Laboratoire Jacques-Louis Lions)

  • Marie Postel

    (Laboratoire Jacques-Louis Lions)

Abstract

A partial differential equation (PDE) is a relation between a function of several variables and its partial derivatives. In this chapter, we first consider the simplest case of ordinary differential equations (ODE), with a solution depending on a single independent variable (time variable here). We present discrete methods for the numerical integration of ODEs. These methods (or numerical schemes) are then used to study three PDEs, depending both on time and space variables, modeling convection, wave and heat propagation.

Suggested Citation

  • Ionut Danaila & Pascal Joly & Sidi Mahmoud Kaber & Marie Postel, 2023. "Numerical Approximation of Model Partial Differential Equations," Springer Books, in: An Introduction to Scientific Computing, edition 2, chapter 0, pages 1-34, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-35032-0_1
    DOI: 10.1007/978-3-031-35032-0_1
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