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Effective order of partitioned Runge-Kutta methods. (English) Zbl 1429.65143
Summary: In this paper, partitioned Runge-Kutta methods of effective order 4 with three stages are constructed. The most obvious feature of these methods is efficiency in terms of implementation cost. The numerical results verify that the asymptotic error behavior of the effective order 4 partitioned Runge-Kutta methods with three stages is similar to that of classical order 4 methods which necessarily require four stages. Moreover, it is evident from the numerical results that effective order methods are more efficient than their classical order counterpart.
MSC:
65L05 Numerical methods for initial value problems
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
Software:
DESIRE
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