Numerical solution methods for implicit Runge-Kutta methods of arbitrarily high order

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Owe Axelsson Maya Neytcheva


In this study we consider an efficient implementation of Implicit Runge-Kutta methods for solving large systems of ordinary differential equations that originate from finite element discretization of the heat and similar equations, to be solved on large time intervals. The main contribution of this work is to show how to implement a fully stage-parallel version of the method, utilizing the dominance of the block lower triangular part of the quadrature matrix, and to illustrate it numerically. Its usage for the solution of algebraic-differential equations is also touched.

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Axelsson, O., & Neytcheva, M. (2020). Numerical solution methods for implicit Runge-Kutta methods of arbitrarily high order. Proceedings Of The Conference Algoritmy, , 11 - 20. Retrieved from


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