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