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An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection

Josef DalíkHelena Růžičková — 1995

Applications of Mathematics

We describe a numerical method for the equation u t + p u x - ε u x x = f in ( 0 , 1 ) × ( 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.

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