Solving a Differential Equation by a Legendre Spectral Method

Ionut Danaila (), Pascal Joly, Sidi Mahmoud Kaber and Marie Postel
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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

Chapter Chapter 6 in An Introduction to Scientific Computing, 2023, pp 129-143 from Springer

Abstract: 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.

Date: 2023
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DOI: 10.1007/978-3-031-35032-0_6

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