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Numerical solutions of the reaction diffusion system by using exponential cubic B-spline collocation algorithms

100%
Ersoy O., Dag I.
Open Physics
|
2015
|
vol. 13
|
issue 1
EN
The solutions of the reaction-diffusion system are given by method of collocation based on the exponential B-splines. Thus the reaction-diffusion systemturns into an iterative banded algebraic matrix equation. Solution of the matrix equation is carried out byway of Thomas algorithm. The present methods test on both linear and nonlinear problems. The results are documented to compare with some earlier studies by use of L∞ and relative error norm for problems respectively.
2
Content available remote

Travelling wave solutions: A new approach to the analysis of nonlinear physical phenomena

100%
Sayevand K., Baleanu D., Fardi M.
Open Physics
|
2014
|
vol. 12
|
issue 7
480-489
EN
In this manuscript, a reliable scheme based on a general functional transformation is applied to construct the exact travelling wave solution for nonlinear differential equations. Our methodology is investigated by means of the modified homotopy analysis method which contains two convergence-control parameters. The obtained results reveal that the proposed approach is a very effective. Several illustrative examples are investigated in detail.
3
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Analytical approximate solutions to the Thomas-Fermi equation

86%
Marinca V., Ene R.-D.
Open Physics
|
2014
|
vol. 12
|
issue 7
503-510
EN
The purpose of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to solve the nonlinear differential Thomas-Fermi equation. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. An excellent agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.
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