Explicit Runge–Kutta methods for starting integration of Lane–Emden problem

Ch. Tsitouras

Applied Mathematics and Computation, 2019, vol. 354, issue C, 353-364

Abstract: Traditionally, when constructing explicit Runge–Kutta methods we demand the satisfaction of the trivial simplifying assumption. Thus, f1=f(x0,y0) is always used as the first stage of these methods when applied to the Initial Value Problem (IVP): y′(x)=f(x,y),y(x0)=y0. Here we examine the case with f1=f(x0+c1h,y0),(h: the step) and c1 ≠ 0. We derive the order conditions for arbitrary order and construct a 5th order method at the standard cost of six stages per step. This method is found to outperform other classical Runge–Kutta pairs with orders 5(4) when applied to problems with singularity at the beginning (e.g. Lane–Emden problem).

Keywords: Runge–Kutta; 5th order; Row simplifying assumptions; Rooted trees; 2-colored leaves; Lane–Emden problem (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:354:y:2019:i:c:p:353-364

DOI: 10.1016/j.amc.2019.02.047

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