Multidomain pseudospectral methods for nonlinear convection-diffusion equations
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Multidomain pseudospectral approximations to nonlinear convection-diffusion equations are considered. The schemes are formulated with the Legendre-Galerkin method, but the nonlinear term is collocated at the Legendre/Chebyshev-Gauss-Lobatto points inside each subinterval. Appropriate base functions are introduced so that the matrix of the system is sparse, and the method can be implemented efficiently and in parallel. The stability and the optimal rate of convergence of the methods are proved. Numerical results are given for both the single domain and the multidomain methods to make a comparison.
Key wordsmultidomain Legendre/Chebyshev collocation convection-diffusion equation
Chinese Library ClassificationO241.82
2010 Mathematics Subject Classification65M70 35L65 35L50
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