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K. Aruna

Bio: K. Aruna is an academic researcher from VIT University. The author has contributed to research in topics: Nonlinear system & Boundary value problem. The author has an hindex of 9, co-authored 15 publications receiving 510 citations.

Papers
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Journal ArticleDOI
TL;DR: This paper implemented relatively new, exact series method of solution known as the differential transform method for solving linear and nonlinear Klein–Gordon equation.

115 citations

Journal ArticleDOI
TL;DR: In this article, the authors proposed a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schrodinger equations based mainly on two-dimensional differential transform method which is one of the approximate methods.
Abstract: In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schrodinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.

109 citations

Journal ArticleDOI
TL;DR: Comparison of the obtained results with exact solutions shows that the variational iteration method used is an effective and highly promising method for treating various classes of both linear and nonlinear singular boundary value problems.
Abstract: This paper applies He's variational iteration method for solving nonlinear singular boundary value problems. The solution process is illustrated and various physically relevant results are obtained. Comparison of the obtained results with exact solutions shows that the method used is an effective and highly promising method for treating various classes of both linear and nonlinear singular boundary value problems.

108 citations

Journal ArticleDOI
TL;DR: In this article, the authors implemented a relatively new, exact series method of solution known as the differential transform method for solving singular two-point boundary value problems, and several illustrative examples are given to demonstrate the effectiveness of the present method.

76 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a reliable algorithm to develop exact and approximate solutions for the linear and non-linear systems of partial differential equations based mainly on two-dimensional differential transform method.

67 citations


Cited by
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Book ChapterDOI
01 Jan 2015

3,828 citations

Journal ArticleDOI
TL;DR: A reliable new algorithm of DTM is proposed, namely multi-step DTM, which will increase the interval of convergence for the series solution, and is applied to Lotka-Volterra, Chen and Lorenz systems.
Abstract: The differential transform method (DTM) is an analytical and numerical method for solving a wide variety of differential equations and usually gets the solution in a series form. In this paper, we propose a reliable new algorithm of DTM, namely multi-step DTM, which will increase the interval of convergence for the series solution. The multi-step DTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. This new algorithm is applied to Lotka-Volterra, Chen and Lorenz systems. Then, a comparative study between the new algorithm, multi-step DTM, classical DTM and the classical Runge-Kutta method is presented. The results demonstrate reliability and efficiency of the algorithm developed.

196 citations

Journal ArticleDOI
TL;DR: In this paper, a local fractional series expansion method was used to solve the Klein-Gordon equations on Cantor sets within the local fractionals derivatives, and the analytical solutions within the non-differential terms were discussed.
Abstract: We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.

134 citations