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

  1. Cano, Begoña
  2. Moreta, María Jesús 1
  1. 1 Universidad Complutense de Madrid
    info

    Universidad Complutense de Madrid

    Madrid, España

    ROR 02p0gd045

Revista:
ESAIM: Mathematical Modelling and Numerical Analysis

ISSN: 2822-7840,  2804-7214

Any de publicació: 2024

Volum: 58

Número: 3

Pàgines: 1053-1085

Tipus: Article

DOI: 10.1051/M2AN/2024011 GOOGLE SCHOLAR lock_openAccés obert editor

Altres publicacions en: ESAIM: Mathematical Modelling and Numerical Analysis

Resum

In this paper a technique is given to recover the classical order of the method when explicitexponential Runge–Kutta methods integrate reaction-diffusion problems. In the literature, methods ofhigh enough stiff order for problems with vanishing boundary conditions have been constructed, butthat implies restricting the coefficients and thus, the number of stages and the computational costmay significantly increase with respect to other methods without those restrictions. In contrast, thetechnique which is suggested here is cheaper because it just needs, for any method, to add some termswith information only on the boundaries. Moreover, time-dependent boundary conditions are directlytackled here

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