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Journal Paper

A Modification of He’s Variational Iteration Method by Taylor’s Series for Solving Second-Order Nonlinear Partial Differential Equations

Journal of Interpolation and Approximation in Scientific Computing, 2013 (2013) 1-7.

In this work, a modification of He’s variational iteration method by Taylor’s series is used for finding the solution of the second order nonlinear partial differential  equations. This modification expands the application of variational iteration method for those nonlinear equations which have logarithmic or trigonometric nonlinear part. To show the efficiency of the method, several examples are presented.

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Journal Paper

Solution for Partial Differential Equations Involving Logarithmic Nonlinearities

Australian Journal of Basic and Applied Sciences, Vol. 5 Apr., (2011) 60-66.

In this paper, a modification of He’s variational iteration method by using r terms of Taylor’s series is applied for finding the solution of Kolmogorov-Petrovskii-Piskunov and Klein-Gordon equations with logarithmic  non-linearities. This modification cause to the new application of the variational iteration method for equations with logarithmic nonlinear part. To show the efficiency of the method, several examples are presented.

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conference paper

A New Approach of a Variational Iteration Method for Nonlinear Partial Differential Equations with Exponential Nonlinearity

41st Annual Iranian Mathematics Conference  (AIMC41), (2010), Urmia, Iran.

In this work, new approach of the variational iteration method by using $r$ terms of Taylor’s series is applied for solving nonlinear partial differential equations with exponential non-linearity. Numerical results are revealing its effectiveness and simplicity.

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conference paper

Solution for Partial Differential Equations Involving Logarithmic Nonlinearities

International Conference on Mathematical Applications in Engineering (ICMAE’10), (2010), Kuala Lumpur, Malaysia.

Recently nonlinear partial differential equation has attracted scientist’s attention, which means that this type of equations playes a keyrole in many fields such as engineering. In this work we considered the variational iteration method which is an usefull instrument for solving partial differential equations
with polynomials nonlinearities. This method first proposed by He and it was used for solving many kinds of situations. We have made a modification on the (VIM) in order to apply it for those PDE’s with logarithmic nonlinearities. We employed this modified method for solving the Klein-Gordon equation and the Kolmogorov-Petrovskii-Piskunov equation which are two applicable equations. Klein-Gordon was named after the physicists Oskar Klein and Walter Gordon, who in 1927 proposed that it describes relativistic electrons. One of the best known model equations with dissipation is the equation suggested in 1937 by Kolmogorov, Petrovskii and Piskunov. This equation describes such phenomena as combustion (physics) and propagation of concentration waves. This method could be used for any nonlinear partial differential equation with logarithmic nonlinearitie. The results reveal that the method is very effective and convenient.

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