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    Öğe
    A comparative study of numerical methods for solving (n+1) dimensional and third-order partial differential equations
    (American Scientific Publishers, 2016) Acan, Omer; Keskin, Yildiray
    In this study, we compare the reduced differential transform method and the variational iteration method. This has been achieved by handling (2+1) dimensional and third-order type of the Zakharov-Kuznetsov ZK(m,m) partial differential equations. Two numerical examples have also been carried out to validate and demonstrate efficiency of the two methods. Also, it is shown that the reduced differential transform method has advantage over variational iteration method. This method is very fast, efficient, applicable and has powerful effects in linear and nonlinear problems. © 2016 American Scientific Publishers All rights reserved.
  • [ X ]
    Öğe
    Conformable variational iteration method, conformable fractional reduced differential transform method and conformable homotopy analysis method for non-linear fractional partial differential equations
    (Taylor & Francis Ltd, 2020) Acan, Omer; Firat, Omer; Keskin, Yildiray
    In this paper, we introduce conformable variational iteration method (C-VIM), conformable fractional reduced differential transform method (CFRDTM) and conformable homotopy analysis method (C-HAM). Between these methods, the C-VIM is introduced for the first time for fractional partial differential equations (FPDEs). These methods are new versions of well-known VIM, RDTM and HAM. In addition, above-mentioned techniques are based on new defined conformable fractional derivative to solve linear and non-linear conformable FPDEs. Firstly, we present some basic definitions and general algorithm for proposal methods to solve linear and non-linear FPDEs. Secondly, to understand better, the presented new methods are supported by some examples. Finally, the obtained results are illustrated by the aid of graphics and the tables. The applications show that these new techniques C-VIM, CFRDTM and C-HAM are extremely reliable and highly accurate and it provides a significant improvement in solving linear and non-linear FPDEs.