An inverse eigenvalue problem: ComputingB-stable Runge-Kutta methods having real poles |
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Authors: | Michael Müller |
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Institution: | (1) Institut für Praktische Mathematik, Universität Karlsruhe, 7500 Karlsruhe, Germany |
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Abstract: | The implementation of implicit Runge-Kutta methods requires the solution of large sets of nonlinear equations. It is known that on serial machines these costs can be reduced if the stability function of ans-stage method has only ans-fold real pole. Here these so-called singly-implicit Runge-Kutta methods (SIRKs) are constructed utilizing a recent result on eigenvalue assignment by state feedback and a new tridiagonalization, which preserves the entries required by theW-transformation. These two algorithms in conjunction with an unconstrained minimization allow the numerical treatment of a difficult inverse eigenvalue problem. In particular we compute an 8-stage SIRK which is of order 8 andB-stable. This solves a problem posed by Hairer and Wanner a decade ago. Furthermore, we finds-stageB-stable SIRKs (s=6,8) of orders, which are evenL-stable. |
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Keywords: | Mathematics Subject Classification 65F15 65F30 65L20 |
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