Cano, BegoñaMoreta Santos, María Jesús2024-12-102024-12-102024-09-24B. Cano y M. J. Moreta. Simplified explicit Exponential Runge-Kutta methods without order reduction, Journal of Computational mathematics (JCM) (2024). 4 Actividad investigadora 11 DOI:10.4208/jcm.2407-m2023-0131.0254-940910.4208/jcm.2407-m2023-0131https://hdl.handle.net/20.500.14352/112283In a previous paper, a technique was suggested to avoid order reduction with any explicit exponential Runge-Kutta method when integrating initial boundary value nonlinear problems with time-dependent boundary conditions. In this paper, we significantly simplify the full discretization formulas to be applied under conditions which are nearly always satisfied in practice. Not only a simpler linear combination of ϕj -functions is given for both the stages and the solution, but also the information required on the boundary is so much simplified that, in order to get local order three, it is no longer necessary to resort to numerical differentiation in space. In many cases, even to get local order 4. The technique is then shown to be computationally competitive against other widely used methods with high enough stiff order through the standard method of lines.engjournal article1991-7139https://dx.doi.org/10.4208/jcm.2407-m2023-0131restricted access519.6Exponential Runge-Kutta methodsAvoiding order reduction in timeEfficiencyMatemáticas (Matemáticas)Análisis numérico1206 Análisis Numérico1206.13 Ecuaciones Diferenciales en Derivadas Parciales