Adaptive nested implicit Runge–Kutta formulas of Gauss type

This paper deals with a special family of implicit Runge–Kutta formulas of orders 2, 4 and 6. These methods are of Gauss type; i.e., they are based on Gauss quadrature formulas of orders 2, 4 and 6, respectively. However, the methods under discussion have only explicit internal stages that lead to c...

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Bibliographic Details
Published in:	Applied numerical mathematics Vol. 59; no. 3; pp. 707 - 722
Main Authors:	Kulikov, G.Yu, Shindin, S.K.
Format:	Journal Article Conference Proceeding
Language:	English
Published:	Kidlington Elsevier B.V 01.03.2009 Elsevier
Subjects:	Almost symplectic integration Approximations and expansions Exact sciences and technology Gauss-type methods Local error estimation Mathematical analysis Mathematics Measure and integration Nested implicit Runge–Kutta formulas Numerical analysis Numerical analysis. Scientific computation Numerical approximation Ordinary differential equations Real functions Sciences and techniques of general use 65L05 65L06 Nested implicit Runge–Kutta formulas Gauss-type methods Ordinary differential equations Local error estimation Almost symplectic integration Numerical integration Error estimation Differential equation Gauss method Runge Kutta method Gauss formula Nested implicit Runge-Kutta formulas Implementation Numerical approximation Numerical analysis Cubature Applied mathematics Quadrature formula Hamiltonian 65L06 Ordinary differential equations
ISSN:	0168-9274, 1873-5460
Online Access:	Get full text
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