A modified perturbation solution to the one-dimensional Bratu problem
作者：
Highlights：
• An approximate analytical solution to the one-dimensional Bratu boundary value problem is introduced in this paper.
• The solution is based on some perturbation methods where artificial parameter is embedded to expand a dependent variable.
• Modifications are introduced to implement some techniques to solve a boundary value problem with different nonlinearities.
• The current solution gives good convergence compared with the exact lower branch solution at any value of Bratu constant.
• Its recursive nature allows for more iteration with more correction terms added to the final solution, i.e. more accuracy.
摘要
•An approximate analytical solution to the one-dimensional Bratu boundary value problem is introduced in this paper.•The solution is based on some perturbation methods where artificial parameter is embedded to expand a dependent variable.•Modifications are introduced to implement some techniques to solve a boundary value problem with different nonlinearities.•The current solution gives good convergence compared with the exact lower branch solution at any value of Bratu constant.•Its recursive nature allows for more iteration with more correction terms added to the final solution, i.e. more accuracy.
论文关键词：Perturbation method,Bratu problem,Nonlinear boundary value problem
论文评审过程：Available online 2 March 2019, Version of Record 2 March 2019.
论文官网地址：https://doi.org/10.1016/j.amc.2019.02.026
