Construction of Runge–Kutta type methods for solving ordinary differential equations

In this paper, we study Runge–Kutta methods with continuous stage, introduced by Butcher in 1987. By setting the coefficients of this family of methods and choosing the appropriate numerical integration, we derive new classes of Runge–Kutta methods. Furthermore, we extend the W-transformation techni...

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Vydáno v:Applied mathematics and computation Ročník 234; s. 179 - 191
Hlavní autoři: Tang, Wensheng, Sun, Yajuan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 15.05.2014
Témata:
(Conjugate) Symplectic method
Computation
Conjugates
Construction
Differential equations
Energy-preserving method
Hamiltonian system
Mathematical models
Numerical integration
Runge-Kutta method
Runge–Kutta method with continuous stage
Symmetric method
W-transformation
Energy-preserving method
Hamiltonian system
(Conjugate) Symplectic method
Runge–Kutta method with continuous stage
Symmetric method
W-transformation
ISSN:0096-3003, 1873-5649
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Shrnutí:In this paper, we study Runge–Kutta methods with continuous stage, introduced by Butcher in 1987. By setting the coefficients of this family of methods and choosing the appropriate numerical integration, we derive new classes of Runge–Kutta methods. Furthermore, we extend the W-transformation technique by permitting W to be a non-square matrix. This allows us to construct more high-order implicit Runge–Kutta methods with some geometric properties. Specially, we provide Runge–Kutta methods with continuous stage which are (conjugate) symplectic, symmetric or energy-preserving for solving Hamiltonian systems. We also present some numerical experiments to verify our results.
Bibliografie:ObjectType-Article-2
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.02.042