Solving reaction-diffusion problems with explicit Runge–Kutta exponential methods without order reduction

Cano, BegoñaMoreta Santos, María Jesús2024-12-092024-12-092024-06-18B. Cano y M. J. Moreta. Solving reaction-diffusion problems with explicit Runge-Kutta exponential methods without order reduction, ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 58 (2024), 1053 – 1085.2822-784010.1051/m2an/2024011https://hdl.handle.net/20.500.14352/112200In this paper a technique is given to recover the classical order of the method when explicit exponential Runge–Kutta methods integrate reaction-diffusion problems. In the literature, methods of high enough stiff order for problems with vanishing boundary conditions have been constructed, but that implies restricting the coefficients and thus, the number of stages and the computational cost may significantly increase with respect to other methods without those restrictions. In contrast, the technique which is suggested here is cheaper because it just needs, for any method, to add some terms with information only on the boundaries. Moreover, time-dependent boundary conditions are directly tackled here.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Solving reaction-diffusion problems with explicit Runge–Kutta exponential methods without order reductionjournal article2804-7214https://doi.org/10.1051/m2an/2024011open access519.6Exponential Runge–Kutta methodsNonlinear reaction-diffusion problemsAvoiding order reduction in timeMatemáticas (Matemáticas)Análisis numérico1206.13 Ecuaciones Diferenciales en Derivadas Parciales1206 Análisis Numérico