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Chapter 5: Orthogonal Collocation and Pseudospectral Foundations

From Gaussian quadrature to Legendre pseudospectral transcription

Low-order collocation is local and transparent, but smooth trajectories can be represented far more efficiently with global polynomials. This chapter builds the required approximation theory in layers: orthogonal collocation, Legendre polynomials, Lagrange interpolation, Gaussian quadrature, and differentiation matrices. Those ingredients then lead naturally to the LGL, LG, and LGR pseudospectral schemes.

Chapter contents

  1. Orthogonal Collocation and Gaussian Quadrature

  2. Legendre Polynomials, Lagrange Interpolation, and Gaussian Quadrature

  3. Gaussian Quadrature Weights and LGL Pseudospectral Methods

  4. The Legendre–Gauss Pseudospectral Method

  5. The Legendre–Gauss–Radau Pseudospectral Method

  6. Exercises

Chapter 4: Direct Numerical Methods and Collocation
Exercises
Chapter 5: Orthogonal Collocation and Pseudospectral Foundations
Orthogonal Collocation and Gaussian Quadrature