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oai:uvadoc.uva.es:10324/732542025-01-09T20:06:14Zcom_10324_1176com_10324_931com_10324_894col_10324_1359

Efficient exponential Rosenbrock methods till order four Cano Urdiales, Begoña Moreta Santos, María Jesús Producción Científica In a previous paper, a technique was described to avoid order reduction with exponential Rosenbrock methods when integrating initial boundary value problems with time-dependent boundary conditions. That requires to calculate some information on the boundary from the given data. In the present paper we prove that, under some assumptions on the coefficients of the method which are mainly always satisfied, no numerical differentiation is required to approximate that information in order to achieve order 4 for parabolic problems with Dirichlet boundary conditions. With Robin/Neumann ones, just numerical differentiation in time may be necessary for order 4, but none for order ≤ 3. Furthermore, as with this technique it is not necessary to impose any stiff order conditions, in search of efficiency, we recommend some methods of classical orders 2, 3 and 4 and we give some comparisons with several methods in the literature, with the corresponding stiff order. 2025-01-09T07:17:20Z 2025-01-09T07:17:20Z 2025 info:eu-repo/semantics/article Journal of Computational and Applied Mathematics, enero 2025, vol. 453, 116158 0377-0427 https://uvadoc.uva.es/handle/10324/73254 10.1016/j.cam.2024.116158 116158 Journal of Computational and Applied Mathematics 453 eng https://www.sciencedirect.com/science/article/pii/S0377042724004072 info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ © 2024 The Author(s) Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier SI