On the convergence of numerical blow-up time for a second order nonlinear ordinary differential equation

DOI10.1016/j.aml.2010.08.011zbMath1209.65082OpenAlexW2081867608WikidataQ115360912 ScholiaQ115360912MaRDI QIDQ607147

Chien-Hong Cho

Publication date: 19 November 2010

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

Full work available at URL: https://doi.org/10.1016/j.aml.2010.08.011

zbMATH Keywords

convergenceblow-uperror estimatefinite difference methods

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) Error bounds for numerical methods for ordinary differential equations (65L70) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (10)

Provable convergence of blow-up time of numerical approximations for a class of convection-diffusion equations ⋮ On the computation of the numerical blow-up time ⋮ A numerical algorithm for blow-up problems revisited ⋮ Non-monotonic blow-up problems: test problems with solutions in elementary functions, numerical integration based on non-local transformations ⋮ The series expansions and blow-up time estimation for the solutions of convolution Volterra-Hammerstein integral equations ⋮ Convergence Analysis for a Three-Level Finite Difference Scheme of a Second Order Nonlinear ODE Blow-Up Problem ⋮ Numerical blow-up analysis of linearly implicit Euler method for nonlinear parabolic integro-differential equations ⋮ Stability for the finite difference schemes of the linear wave equation with nonuniform time meshes ⋮ Numerical blow-up analysis of the explicit L1-scheme for fractional ordinary differential equations ⋮ Nonlinear problems with blow-up solutions: numerical integration based on differential and nonlocal transformations, and differential constraints

Cites Work

• Further remarks on asymptotic behavior of the numerical solutions of parabolic blow-up problems
• Blowing up of a finite difference solution to \(u_t=u_{xx}+u^2\)
• On the finite difference approximation for a parabolic blow-up problem
• Numerical method of estimating the blow-up time and rate of the solution of ordinary differential equations -- an application to the blow-up problems of partial differential equations
• The Euler method in the numerical integration of reaction-diffusion problems with blow up
• Asymptotic behaviour for a numerical approximation of a parablic problem with blowing up solutions

This page was built for publication: On the convergence of numerical blow-up time for a second order nonlinear ordinary differential equation