𝔖 Bobbio Scriptorium
✦   LIBER   ✦

New embedded explicit pairs of exponentially fitted Runge–Kutta methods

✍ Scribed by A. París; L. Rández

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
348 KB
Volume
234
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

Two new embedded pairs of exponentially fitted explicit Runge-Kutta methods with four and five stages for the numerical integration of initial value problems with oscillatory or periodic solutions are developed. In these methods, for a given fixed ω the coefficients of the formulae of the pair are selected so that they integrate exactly systems with solutions in the linear space generated by {sinh(ωt), cosh(ωt)}, the estimate of the local error behaves as O(h 4 ) and the high-order formula has fourth-order accuracy when the stepsize h → 0.

These new pairs are compared with another one proposed by Franco [J.M. Franco, An embedded pair of exponentially fitted explicit Runge-Kutta methods, J. Comput. Appl. Math. 149 (2002) 407-414] on several problems to test the efficiency of the new methods.

📜 SIMILAR VOLUMES

Structure preservation of exponentially
Structure preservation of exponentially fitted Runge–Kutta methods
✍ M. Calvo; J.M. Franco; J.I. Montijano; L. Rández 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 227 KB

The preservation of some structure properties of the flow of differential systems by numerical exponentially fitted Runge-Kutta (EFRK) methods is considered. A complete characterisation of EFRK methods that preserve linear or quadratic invariants is given and, following the approach of Bochev and Sc

Sixth-order symmetric and symplectic exp
Sixth-order symmetric and symplectic exponentially fitted Runge–Kutta methods of the Gauss type
✍ M. Calvo; J.M. Franco; J.I. Montijano; L. Rández 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 764 KB

The construction of exponentially fitted Runge-Kutta (EFRK) methods for the numerical integration of Hamiltonian systems with oscillatory solutions is considered. Based on the symplecticness, symmetry, and exponential fitting properties, two new threestage RK integrators of the Gauss type with fixed