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An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection. (English) Zbl 0842.65057

Authors’ summary: We describe a numerical method for the equation \(u_t+ pu_x- \varepsilon u_{xx}= f\) in \((0, 1)\times (0, T)\) with Dirichlet boundary and initial conditions which is a combination of the method of characteristics and the finite difference method. We prove both an a priori local error-estimate of a high-order and stability. Example 3.3 indicates that our approximate solutions are disturbed only by a minimal amount of the artificial diffusion.
Reviewer: S.Jiang (Bonn)

MSC:

65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
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References:

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