Algebraic Order for Some Exponentially–Fitted Explicit Runge–Kutta Methods

Article type: Research Article

Authors: Franco, J.M.^{; 1}

Affiliations: Departamento de Matemática Aplicada, C.P.S. de Ingeniería, Universidad de Zaragoza, María de Luna 3, 50015 Zaragoza, Spain

Note: [1] E-mail: jmfranco@posta.unizar.es.

Abstract: Some exponentially–fitted explicit Runge–Kutta methods specially adapted to the numerical integration of IVPs with oscillatory solutions are analyzed. The theoretical and numerical results obtained for the Runge–Kutta approach of Simos and coworkers [1, 6] and for the Runge–Kutta approach of Vanden Berghe et al. [9] confirm that they are of algebraic fourth order. These two different procedures for developing exponentially–fitted Runge–Kutta methods have been compared in some numerical examples.

Keywords: Adapted Runge–Kutta methods, exponential fitting, oscillatory initial value problems

Keywords: 65L05, 65L06

DOI: 10.3233/JCM-2003-3105

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 3, no. 1, pp. 55-71, 2003