Solving the one dimensional Bratu problem with efficient fourth order iterative methods

SeMA Journal ◽  
2015 ◽  
Vol 71 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Natalia Romero
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
One Dimensional ◽  
The One ◽  
Bratu Problem

scholarly journals Fourth-Order Deferred Correction Scheme for Solving Heat Conduction Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
D. Yambangwai ◽  
N. P. Moshkin
Keyword(s):  
Fourth Order ◽  
Heat Conduction Problem ◽  
Correction Method ◽  
Dirichlet Boundary Conditions ◽  
Heat Conducting ◽  
One Dimensional ◽  
Deferred Correction ◽  
The Stability ◽  
The One ◽  
Nicolson Scheme

A deferred correction method is utilized to increase the order of spatial accuracy of the Crank-Nicolson scheme for the numerical solution of the one-dimensional heat equation. The fourth-order methods proposed are the easier development and can be solved by using Thomas algorithms. The stability analysis and numerical experiments have been limited to one-dimensional heat-conducting problems with Dirichlet boundary conditions and initial data.

A modified perturbation solution to the one-dimensional Bratu problem

2019 ◽  
Vol 354 ◽  
pp. 296-304 ◽  
Author(s):  
Mina B. Abd-el-Malek ◽  
Amr Abdelrazek ◽  
Mohammed Ghazy ◽  
Gehad Gamal
Keyword(s):  
Perturbation Solution ◽  
One Dimensional ◽  
The One ◽  
Bratu Problem

scholarly journals Γ-limit for the extended Fisher–Kolmogorov equation

2002 ◽  
Vol 132 (1) ◽  
pp. 141-162 ◽  
Author(s):  
D. Hilhorst ◽  
L. A. Peletier ◽  
R. Schätzle
Keyword(s):  
Fourth Order ◽  
Lyapunov Functional ◽  
Transition Energy ◽  
Kolmogorov Equation ◽  
One Dimensional ◽  
Cahn Equation ◽  
Area Functional ◽  
The One ◽  
Image Position

We consider the Lyapunov functional, of the rescaled Extended Fisher-Kolmogorov equation This is a fourth order generalization of the Fisher–Kolmogorov or Allen–Cahn equation. We prove that if ε → 0, then tends to the area functional in the sense of Γ-limits, where the transition energy is given by the one-dimensional kink of the Extended Fisher–Kolmogorov equation.

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