Practical Runge--Kutta methods for scientific computation

John Butcher


Implicit Runge–Kutta methods have a special role in the numerical solution of stiff problems, such as those found by applying the method of lines to the partial differential equations arising in physical modelling. Of particular interest in this paper are the high order methods based on Gaussian quadrature and the efficiently implementable singly-implicit methods



implicit Runge–Kutta methods, implicit Euler method, stiff problems, A-stability, L-stability, method of line, Gauss-Legendre quadrature, DIRK methods, SIRK methods, Laguerre polynomials


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.