Numerical methods for evolutionary convection-diffusion problems with nonlinear reaction terms

  1. Bujanda, B. 1
  2. Jorge, J.C. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad Pública de Navarra
    info

    Universidad Pública de Navarra

    Pamplona, España

    ROR https://ror.org/02z0cah89

Book:
Parallel processing applied mathematics

ISBN: 3-540-43792-4

Year of publication: 2002

Volume: 2328

Pages: 833-840

Type: Book chapter

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SCOPUS: 2-s2.0-1442309836 WoS: WOS:000180067200093 GOOGLE SCHOLAR

Abstract

In this paper some new linearly implicit methods are designed to solve evolutionary convection-diffusion problems with non linear reaction terms. Such methods combine the advantages of Alternating Direction Implicit methods and of Additive Runge-Kutta methods, which Cooper & Sayfy introduced (see [6], [7]) to solve non linear stiff problems with linearly implicit schemes. These new methods have an optimal order of computational complexity per time step and besides, under suitable smoothness requirements on the reaction terms, are unconditionally convergent. Some numerical experiences are shown confirming the expected efficiency and robustness of our methods.