Geodesic
An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection
Applications of Mathematics, Tome 40 (1995) no. 5, pp. 367-380.

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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.
DOI : 10.21136/AM.1995.134300
Classification : 35K15, 65M06, 65M12, 65M15, 65M25
Keywords: method of characteristics; finite differences; convection-diffusion problem; local error-estimate; stability 
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     title = {An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection},
     journal = {Applications of Mathematics},
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Dalík, Josef; Růžičková, Helena. An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection. Applications of Mathematics, Tome 40 (1995) no. 5, pp. 367-380. doi : 10.21136/AM.1995.134300. http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134300/

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