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Hasan, M. Kamrul; Ahamed, M. Suzan; Haque, B. M. Ikramul; Alam, M. S.; Hossain, M. Bellal

A higher order implicit method for numerical solution of singular initial value problems. (English) Zbl 1442.65128

Giri, Debasis (ed.) et al., Mathematics and computing. Third international conference, ICMC 2017, Haldia, India, January 17–21, 2017. Proceedings. Singapore: Springer. Commun. Comput. Inf. Sci. 655, 255-264 (2017).
Summary: Recently a lower order implicit method has been presented for solving singular initial value problem. In this article a higher order implicit method has been developed to solve first or higher order problems having an initial singular point. This method is more suitable than second, third and two-stage fourth order implicit Runge-Kutta methods for first order problems. The method also provides significantly better results than the existing lower order implicit method for second order problems.
For the entire collection see [Zbl 1411.65007].

Cited in 1 Document

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations

Keywords:

singular initial value problems; implicit Runge-Kutta method; Lane-Emden-type equation; Emden-Fowler-type equation

Software:

avalanche.f
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Full Text: DOI

References:

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