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

作者：

Highlights：

• Cauchy problems for nonlinear ODEs are studied.

• Blow-up problems and solutions are considered.

• Several new methods of numerical integration are described.

• Differential and nonlocal transformations are used.

• First-order differential constraints are applied.

摘要

•Cauchy problems for nonlinear ODEs are studied.•Blow-up problems and solutions are considered.•Several new methods of numerical integration are described.•Differential and nonlocal transformations are used.•First-order differential constraints are applied.

论文关键词：Blow-up solutions,Nonlinear ordinary differential equations,Cauchy problem,Numerical integration,Nonlocal transformations,Painlevé equations

论文评审过程：Received 19 May 2017, Revised 18 March 2018, Accepted 28 April 2018, Available online 21 May 2018, Version of Record 21 May 2018.

论文官网地址：https://doi.org/10.1016/j.amc.2018.04.071