6533b828fe1ef96bd12878b0
RESEARCH PRODUCT
Generalized singly-implicit Runge-Kutta methods with arbitrary knots
Claus Schneidersubject
Similarity (geometry)Computer Networks and CommunicationsGeneralizationApplied MathematicsComputationMathematical analysisStability (learning theory)Computational MathematicsMatrix (mathematics)Runge–Kutta methodsNonlinear systemSimple (abstract algebra)SoftwareMathematicsdescription
The aim of this paper is to derive Butcher's generalization of singly-implicit methods without restrictions on the knots. Our analysis yields explicit computable expressions for the similarity transformations involved which allow the efficient implementation of the first phase of the method, i.e. the solution of the nonlinear equations. Furthermore, simple formulas for the second phase of the method, i.e. computation of the approximations at the next nodal point, are established. Finally, the matrix which governs the stability of the method is studied.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1985-06-01 | BIT |