An Efficient Fourth Order Implicit Runge-Kutta Algorithm for Second Order Systems

Authors:
Basem S. Attili
Affiliations:
Mathematics Department, University of Sharjah, Sharjah, United Arab Emirates
Venue:
Computer Mathematics
Year:
2008

Citing 6
Cited 0

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Abstract

We will present an algorithmic approach to the implementation of a fourth order two stage implicit Runge-Kutta method to solve periodic second order initial value problems. The systems involved will be solved using some type of factorization that usually involves both complex and real arithmetic. We will consider the real type case which will be efficient and leads to a system that is one fourth the size of similar systems using normal implicit Runge-Kutta method. We will present some numerical examples to show the efficiency of the method.