Transcription of Numerical Methods for Differential Equations
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Numerical Methods for Differential Equations
Numerical Methods for Differential Equations Chapter 5: Partial Differential Equations elliptic and parabolic . Gustaf Soderlind . and Carmen Arevalo Numerical Analysis, Lund University Textbooks: A First Course in the Numerical Analysis of Differential Equations , by Arieh Iserles and Introduction to Mathematical Modelling with Differential Equations , by Lennart Edsberg c Gustaf Soderlind, Numerical Analysis, Mathematical Sciences, Lund University, 2008-09. Numerical Methods for Differential Equations p. 1/50. 1. Brief overview of PDE problems Classification: Three basic types, four prototype Equations Elliptic u = 0 + BC. Parabolic ut = u + BC & IC. Hyperbolic utt = u + BC & IC. ut + a(u)ux = 0 + BC & IC. Numerical Methods for Differential Equations p. 2/50. Classification of PDEs Linear PDE with two independent variables Auxx + 2 Buxy + Cuyy + L(ux , uy , u, x, y) = 0.
Numerical Methods for Differential Equations Chapter 5: Partial differential equations – elliptic and pa rabolic Gustaf Soderlind and Carmen Ar¨ evalo´
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