Abstract
We perform a comparative numerical study of two reaction-diffusion models arising in chemistry by using exponential integrators. Numerical simulations of the reaction kinetics associated with these models, including both the local and global errors as a function of time step and error as a function of computational time are shown.
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References
Ashkenazi, M., Othmer, H.G.: Spatial Patterns in Coupled Biochemical Oscillators. J. Math. Biol. 5, 305–350 (1978)
Berland, H., Skaflestad, B.: Solving the nonlinear Schrödinger equation using exponential integrators. Modeling, Identification and Control 27(4), 201–217 (2006)
Berland, H., Skaflestad, B., Wright, W.: EXPINT — A Matlab package for exponential integrators. Numerics 4 (2005)
Butcher, J.C.: Numerical methods for ordinary differential equations. John Wiley & Sons, Chichester (2003)
Celledoni, E., Marthinsen, A., Qwren, B.: Commutator-free Lie group methods. FGCS 19(3), 341–352 (2003)
Cox, S.M., Matthews, P.C.: Exponential time differencing for stiff systems. J. Comp. Phys. 176(2), 430–455 (2002)
Kepper, P., De Castets, V., Dulos, E., Boissonade, J.: Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction. Physica D 49, 161–169 (1991)
Krogstad, S.: Generalized integrating factor methods for stiff PDEs. Journal of Computational Physics 203(1), 72–88 (2005)
Lawson, D.J.: Generalized Runge-Kutta processes for stable systems with large Lipschitz constants. SIAM J. Numer. Anal. 4, 372–380 (1967)
Lengyel, I., Epstein, I.R.: Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system. Science 251, 650–652 (1991)
Minchev, B., Wright, W.M.: A review of exponential integrators for semilinear problems. Technical Report 2, The Norwegian University of Science and Technology (2005)
Munthe-Kaas, H.: High order Runge-Kutta methods on manifolds. Applied Numerical Mathematics 29, 115–127 (1999)
Nørsett, S.P.: An A-stable modification of the Adams-Bashforth methods. In: Conf. on Numerical solution of Differential Equations, Dundee, pp. 214–219. Springer, Berlin (1969)
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Ştefănescu, R., Dimitriu, G. (2010). Numerical Simulations of Reaction-Diffusion Systems Arising in Chemistry Using Exponential Integrators. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_74
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DOI: https://doi.org/10.1007/978-3-642-12535-5_74
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12534-8
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