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Solving a Differential Equation by a Legendre Spectral Method

In: An Introduction to Scientific Computing

Author

Listed:
  • Ionut Danaila

    (Université de Rouen Normandie, CNRS, Laboratoire de mathématiques Raphaël Salem)

  • Pascal Joly

    (Laboratoire Jacques-Louis Lions)

  • Sidi Mahmoud Kaber

    (Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions)

  • Marie Postel

    (Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions)

Abstract

Spectral methods are approximation techniques for the computation of solutions to ordinary or partial differential equations. They are based on a polynomial expansion of the solution. The precision of these methods is limited only by the regularity of the solution, in contrast to the finite difference and finite element methods. The approximation is based primarily on the weak formulation of the continuous problem. Test functions are polynomials and the integrals involved in the formulation are computed by suitable quadrature formulas. In this chapter, we show how to implement a spectral method to solve a boundary value problem.

Suggested Citation

  • Ionut Danaila & Pascal Joly & Sidi Mahmoud Kaber & Marie Postel, 2023. "Solving a Differential Equation by a Legendre Spectral Method," Springer Books, in: An Introduction to Scientific Computing, edition 2, chapter 0, pages 129-143, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-35032-0_6
    DOI: 10.1007/978-3-031-35032-0_6
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