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

Josef Dalík; Helena Růžičková

Applications of Mathematics (1995)

  • Volume: 40, Issue: 5, page 367-380
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Dalík, Josef, and Růžičková, Helena. "An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection." Applications of Mathematics 40.5 (1995): 367-380. <http://eudml.org/doc/32925>.

@article{Dalík1995,
abstract = {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.},
author = {Dalík, Josef, Růžičková, Helena},
journal = {Applications of Mathematics},
keywords = {method of characteristics; finite differences; convection-diffusion problem; local error-estimate; stability; convection-diffusion problem; method of characteristics; finite difference method; error-estimate; stability},
language = {eng},
number = {5},
pages = {367-380},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection},
url = {http://eudml.org/doc/32925},
volume = {40},
year = {1995},
}

TY - JOUR
AU - Dalík, Josef
AU - Růžičková, Helena
TI - An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 5
SP - 367
EP - 380
AB - 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.
LA - eng
KW - method of characteristics; finite differences; convection-diffusion problem; local error-estimate; stability; convection-diffusion problem; method of characteristics; finite difference method; error-estimate; stability
UR - http://eudml.org/doc/32925
ER -

References

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  4. Accuracy analysis of the eulerian-lagrangian numerical schemes for the convection-diffusion equation, Preprint. 
  5. A finite difference method for a two-dimensional convection-diffusion problem with dominating convection, Submitted to publication. MR1463685
  6. 10.1137/0719063, SIAM J. Numer. Anal. (1982), no. 19, 871–885. (1982) MR0672564DOI10.1137/0719063
  7. Linear and quasilinear equations of parabolic type, Nauka, Moscow, 1967. (Russian) (1967) 
  8. Computational Methods in Ordinary Differential Equations, John Wiley & Sons, London, 1973. (1973) Zbl0258.65069MR0423815
  9. Finite-difference methods for solving the one-dimensional transport equation, Numerical modeling: Application to Marine Systems, J. Noye (ed.), Elsevier, North Holland, 1987, pp. 231–256. (1987) MR0924023
  10. Les méthodes d’élements finis en mécanique des fluides II, 3. Edditions Eyrolles, Paris, 1981. (1981) MR0631851
  11. 10.1007/BF01385788, Numer. Math. (1991), no. 59, 399–412. (1991) MR1113198DOI10.1007/BF01385788

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