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Rahaman, Md. Habibur; Kamrul Hasan, M.; Ali, Md. Ayub; Shamsul Alam, M.

Implicit methods for numerical solution of singular initial value problems. (English) Zbl 1506.65052

Appl. Math. Nonlinear Sci. 6, No. 1, 1-8 (2021).
Summary: Various order of implicit method has been formulated for solving initial value problems having an initial singular point. The method provides better result than those obtained by used implicit formulae developed based on Euler and Runge-Kutta methods. Romberg scheme has been used for obtaining more accurate result.

Cited in 6 Documents

MSC:

65D30 Numerical integration
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
35F10 Initial value problems for linear first-order PDEs
35F25 Initial value problems for nonlinear first-order PDEs
35G10 Initial value problems for linear higher-order PDEs
35G25 Initial value problems for nonlinear higher-order PDEs

Keywords:

singular integrals; Romberg scheme; singular initial value problems; implicit Runge-Kutta method

Software:

avalanche.f
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References:

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