Abstract
In this study we focus on a comparative numerical approach of two reaction-diffusion models arising in biochemistry by using exponential integrators. The goal of exponential integrators is to treat exactly the linear part of the differential model and allow the remaining part of the integration to be integrated numerically using an explicit scheme. Numerical simulations including both the global error as a function of time step and error as a function of computational time are shown.
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References
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., Owren, 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)
Gierer, A., Meinhardt, H.: A theory of biological pattern formation. Kybernetik 12, 30–39 (1972)
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)
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)
Murray, J.D.: Mathematical Biology, 2nd edn. Springer, New York (1993)
Nørsett, S.P.: An A-stable modification of the Adams-Bashforth methods. In: Conf. on Numerical solution of Differential Equations (Dundee, 1969), pp. 214–219. Springer, Berlin (1969)
Thomas, D.: Artificial enzyme membrane, transport, memory and oscillatory phenomena. In: Thomas, D., Kervenez, J.-P. (eds.) Analysis and Control of Immobilised Enzyme Systems, pp. 115–150. Springer, Heidelberg (1975)
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Dimitriu, G., Ştefănescu, R. (2009). Numerical Experiments for Reaction-Diffusion Equations Using Exponential Integrators. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_26
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DOI: https://doi.org/10.1007/978-3-642-00464-3_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00463-6
Online ISBN: 978-3-642-00464-3
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