Summary
This paper discussesrational Runge-Kutta methods for stiff differential equations of high dimensions. These methods are explicit and in addition do not require the computation or storage of the Jacobian. A stability analysis (based onn-dimensional linear equations) is given. A second orderA 0-stable method with embedded error control is constructed and numerical results of stiff problems originating from linear and nonlinear parabolic equations are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hindmarsh, A.C., Byrne, G.D.: Applications of EPISODE. In: Numerical methods for differential systems. L. Lapidus, W.E. Schiesser (eds.), New York: Academic Press, 1976
Wambecq, A.: Rational Runge-Kutta method for solving systems of ordinary differential equations. Computing20, 333–342 (1978)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hairer, E. Unconditionally stable explicit methods for parabolic equations. Numer. Math. 35, 57–68 (1980). https://doi.org/10.1007/BF01396370
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01396370