## An efficient implicit Runge-Kutta method for second order systems.(English)Zbl 1100.65062

Summary: We consider the efficient implementation of a fourth order two stage implicit Runge-Kutta method to solve periodic second order initial value problems. To solve the resulting systems, we use the factorization of the discretized operator. Such proposed factorization involves both complex and real arithmetic. The latter case is considered here. The resulting system is efficient and small in size. It is one fourth the size of systems using normal implicit Runge-Kutta method. Numerical details and examples are also presented to demonstrate the efficiency of the method.

### MSC:

 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
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### References:

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