### APMA 2560 – Spring 2011

Lecture 4

Numerical Solution of PDEs II

Instructor: Professor G.E. Karniadakis

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• Approximation Theory and Resolution Rules-of-Thumb

– Chebyshev polynomials and convergence

– Regular versus singular Sturm-Liuville problems

– Legendre polynomials and convergence

– Laguerre and Hermite polynomials

– Askey family of orthogonal polynomials

• Reading: Gottlieb & Orszag, section 3; also Karniadakis & Sherwin, Appendix A