The implicit Euler method for the numerical solution of singular initial value problems

DOI10.1016/S0168-9274(99)00130-0zbMath0953.65052OpenAlexW2100495513WikidataQ127452611 ScholiaQ127452611MaRDI QIDQ1567643

Othmar Koch, Peter Kofler, Ewa B. Weinmüller

Publication date: 21 June 2000

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(99)00130-0

zbMATH Keywords

stabilityconvergencenumerical examplesimplicit Euler methodasymptotic error expansioniterated defect correction acceleration methodsingular nonlinear initial-value problems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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The convergence of shooting methods for singular boundary value problems ⋮ Numerical approximation for singular second order differential equations ⋮ On numerical methods to second-order singular initial value problems with additive white noise ⋮ Implicit methods for numerical solution of singular initial value problems ⋮ A Higher Order Implicit Method for Numerical Solution of Singular Initial Value Problems ⋮ Unnamed Item ⋮ Analytical and numerical treatment of a singular initial value problem in avalanche modeling. ⋮ Unnamed Item ⋮ Linearization techniques for singular initial-value problems of ordinary differential equations ⋮ A new approach to constructing of explicit one-step methods of high order for singular initial value problems for nonlinear ordinary differential equations ⋮ Piecewise quasilinearization techniques for singular boundary-value problems ⋮ The adapted block boundary value methods for singular initial value problems ⋮ Numerical solution of singular boundary value problems with logarithmic singularities by Padé approximation and collocation methods ⋮ An adaptive pair of one-step hybrid block Nyström methods for singular initial-value problems of Lane-Emden-Fowler type

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