Nonlinear problems with blow-up solutions: numerical integration based on differential and nonlocal transformations, and differential constraints

DOI10.1016/j.amc.2018.04.071zbMath1427.65112arXiv1707.03493OpenAlexW2804157537WikidataQ129788720 ScholiaQ129788720MaRDI QIDQ2335596

Inna K. Shingareva, Andrei D. Polyanin

Publication date: 14 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.03493

zbMATH Keywords

numerical integrationCauchy problemblow-up solutionsPainlevé equationsnonlinear ordinary differential equationsnonlocal transformations

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Growth and boundedness of solutions to ordinary differential equations (34C11) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items

Vanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular point ⋮ A numerical scheme for the blow-up time of solutions of a system of nonlinear ordinary differential equations ⋮ Unnamed Item

Uses Software

• DLMF

Cites Work

• On the criteria for integrability of the Liénard equation
• Parametrically defined nonlinear differential equations, differential-algebraic equations, and implicit ODEs: transformations, general solutions, and integration methods
• Numerical validation of blow-up solutions of ordinary differential equations
• On the convergence of numerical blow-up time for a second order nonlinear ordinary differential equation
• Blow up oscillating solutions to some nonlinear fourth order differential equations
• Theoretical analysis for blow-up behaviors of differential equations with piecewise constant arguments
• An adaptive time step procedure for a parabolic problem with blow-up
• Computation of blowing-up solutions for second-order differential equations using re-scaling techniques
• Difference schemes of optimum degree of implicitness for a family of simple ODEs with blow-up solutions
• The Painlevé property. One century later
• On the Jacobi last multipliers and Lagrangians for a family of Liénard-type equations
• Oscillatory blow-up in nonlinear second order ODE's: The critical case
• Wide oscillation finite time blow up for solutions to nonlinear fourth-order differential equations
• On the computation of blow-up solutions for semilinear ODEs and parabolic PDEs
• Critical points at infinity and blow up of solutions of autonomous polynomial differential systems via compactification
• 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
• On the integrability conditions for a family of Liénard-type equations
• Parametrically defined nonlinear differential equations and their solutions: applications in fluid dynamics
• Nonlocal transformations and linearization of second-order ordinary differential equations
• On the computation of blow-up
• A Compendium of Partial Differential Equation Models
• Maple and Mathematica
• Numerical Solution of Ordinary Differential Equations
• Numerical Methods for Ordinary Differential Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item