Explicit exponential Runge�Kutta methods of high order for parabolic problems

• Autores: Vu Thai Luan, Alexander Ostermann
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 256, Nº 1, 2014, págs. 168-179
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.07.027
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• Resumen

  • Exponential Runge�Kutta methods constitute efficient integrators for semilinear stiff problems. So far, however, explicit exponential Runge�Kutta methods are available in the literature up to order 4 only. The aim of this paper is to construct a fifth-order method.

    For this purpose, we make use of a novel approach to derive the stiff order conditions for high-order exponential methods. This allows us to obtain the conditions for a method of order 5 in an elegant way. After stating the conditions, we first show that there does not exist an explicit exponential Runge�Kutta method of order 5 with less than or equal to 6 stages. Then, we construct a fifth-order method with 8 stages and prove its convergence for semilinear parabolic problems. Finally, a numerical example is given that illustrates our convergence bound.