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An efficient numerical scheme for precise time integration of a diffusion-dissolution/precipitation chemical system. (English) Zbl 1107.65082
Based on an operator splitting method and a dense output event location algorithm, the authors propose a numerical scheme to integrate a diffusion-dissolution/precipitation chemical initial-boundary value problem with jumping nonlinearities. They present a numerical analysis for the scheme and show that it is of order 2 in time. Numerical experiments illustrate the theoretical results.

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
80A30 Chemical kinetics in thermodynamics and heat transfer
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[1] Christophe Besse, Brigitte Bidégaray, and Stéphane Descombes, Order estimates in time of splitting methods for the nonlinear Schrödinger equation, SIAM J. Numer. Anal. 40 (2002), no. 1, 26 – 40. · Zbl 1026.65073 · doi:10.1137/S0036142900381497 · doi.org
[2] Stéphane Descombes, Convergence of a splitting method of high order for reaction-diffusion systems, Math. Comp. 70 (2001), no. 236, 1481 – 1501. · Zbl 0981.65107
[3] S. Descombes and M. Massot, Operator splitting for nonlinear reaction-diffusion systems with an entropic structure : singular perturbation and order reduction, Numerische Mathematik (2004) Vol. 97, No. 4, 667-698. · Zbl 1060.65105
[4] E. Hairer, S. P. Nørsett, and G. Wanner, Solving ordinary differential equations. I, 2nd ed., Springer Series in Computational Mathematics, vol. 8, Springer-Verlag, Berlin, 1993. Nonstiff problems. · Zbl 0789.65048
[5] E. Hairer and G. Wanner, Solving ordinary differential equations. II, Springer Series in Computational Mathematics, vol. 14, Springer-Verlag, Berlin, 1991. Stiff and differential-algebraic problems. · Zbl 0729.65051
[6] Tobias Jahnke and Christian Lubich, Error bounds for exponential operator splittings, BIT 40 (2000), no. 4, 735 – 744. · Zbl 0972.65061 · doi:10.1023/A:1022396519656 · doi.org
[7] E. Maisse, Analyse et simulations numériques de phénomènes de diffusion-dissolution/précipitation en milieux poreux, appliquées au stockage de déchets, Ph.D. thesis, Université Claude Bernard Lyon I, 1998.
[8] E. Maisse and J. Pousin, Diffusion and dissolution/precipitation in an open porous reactive medium, J. Comput. Appl. Math. 82 (1997), no. 1-2, 279 – 290. 7th ICCAM 96 Congress (Leuven). · Zbl 0893.76087 · doi:10.1016/S0377-0427(97)00049-6 · doi.org
[9] G. I. Marchuk, Splitting and alternating direction methods, Handbook of numerical analysis, Vol. I, Handb. Numer. Anal., I, North-Holland, Amsterdam, 1990, pp. 197 – 462. · Zbl 0875.65049
[10] Michelle Schatzman, Toward non commutative numerical analysis: high order integration in time, Proceedings of the Fifth International Conference on Spectral and High Order Methods (ICOSAHOM-01) (Uppsala), 2002, pp. 99 – 116. · Zbl 0999.65095 · doi:10.1023/A:1015140328635 · doi.org
[11] Lawrence F. Shampine, Interpolation for Runge-Kutta methods, SIAM J. Numer. Anal. 22 (1985), no. 5, 1014 – 1027. · Zbl 0592.65041 · doi:10.1137/0722060 · doi.org
[12] Bruno Sportisse, An analysis of operator splitting techniques in the stiff case, J. Comput. Phys. 161 (2000), no. 1, 140 – 168. · Zbl 0953.65062 · doi:10.1006/jcph.2000.6495 · doi.org
[13] Gilbert Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal. 5 (1968), 506 – 517. · Zbl 0184.38503 · doi:10.1137/0705041 · doi.org
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