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A MATLAB implementation of upwind finite differences and adaptive grids in the method of lines. (English) Zbl 1071.65544
Summary: We report on the development of a MATLAB library for the solution of partial differential equation systems following the method of lines. In particular, we focus attention on upwind finite difference schemes and grid adaptivity, i.e., grid movement or grid refinement. Several algorithms are presented and their performance is demonstrated with illustrative examples including a fixed-bed reactor with periodic flow reversal, a model of flame propagation, and the Korteweg-de Vries equation.

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
65Y15 Packaged methods for numerical algorithms
35Q53 KdV equations (Korteweg-de Vries equations)
80A25 Combustion
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
Full Text: DOI
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