Browsing by Subject "ADOMIAN DECOMPOSITION METHOD"

Now showing 1 - 7 of 7
  • No Thumbnail Available
    Item
    Solving the burgers' and regularized long wave equations using the new perturbation iteration technique
    (WILEY) Bildik, N; Deniz, S
    In this study, an efficient framework provided to handle nonlinear partial differential equations by implementing perturbation iteration method. This method is recovered and amended to solve the Burgers' and regularized long wave equations. Comparing our new solutions with the exact solutions reveals that this technique is extremely accurate and effective in solving nonlinear models. Convergence analysis and error estimate are also supplied using some critical theorems.
  • No Thumbnail Available
    Item
    Optimal perturbation iteration method for Bratu-type problems
    (ELSEVIER SCIENCE BV) Deniz, S; Bildik, N
    In this paper, we introduce the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. The proposed method is illustrated by studying Bratu-type equations. Our results show that only a few terms are required to obtain an approximate solution which is more accurate and efficient than many other methods in the literature. (C) 2016 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.
  • No Thumbnail Available
    Item
    Approximate solution of the electrostatic nanocantilever model via optimal perturbation iteration method
    (WILEY) Adel, W; Deniz, S
    In this article, a new technique is used to solve the nonlinear boundary value problem of a cantilever-type nanoelectromechanical system. The technique is called the optimal perturbation iteration method and it is used to solve the problem in the form of a nonlinear differential equation with negative power-law nonlinearity. A convergence and error estimation of the proposed method is presented proving that the method is convergent. Results for the application of the proposed technique are demonstrated through two examples and the tables and figures prove that the method is efficient and straightforward.
  • No Thumbnail Available
    Item
    A compatible Hermite-Taylor matrix-collocation technique with convergence test for second-order partial integro-differential equations containing two independent variables with functional bounds
    (SPRINGER HEIDELBERG) Yalçin, E; Sezer, M
    The aim of this study is to offer a compatible numerical technique to solve second-order linear partial integro-differential equations with variable (functional) bounds, including two independent variables, under the initial and/or boundary conditions by using hybrid Hermite and Taylor series. The method converts the presented integro-differential equation to a matrix equation including the unknown Hermite coefficients. Solving this matrix equation and applying the collocation method, the approximate solution of the problem is obtained in terms of the Hermite polynomials. Also, by means of an error estimation and convergence test related to residual functions, some examples to illustrate the accuracy and efficiency of the method are fulfilled; the obtained results are scrutinized and interpreted. All numerical computations have been performed on the computer programs.
  • No Thumbnail Available
    Item
    A new analytical technique for solving Lane - Emden type equations arising in astrophysics
    (BELGIAN MATHEMATICAL SOC TRIOMPHE) Deniz, S; Bildik, N
    Lane - Emden type equations are nonlinear differential equations which represent many scientific phenomena in astrophysics and mathematical physics. In this study, a new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and performance of the method. This technique provides us to adjust the convergence regions when necessary. Comparing different methods reveals that the proposed method is highly accurate and has great potential to be a new kind of powerful analytical tool for Lane Emden type equations.
  • No Thumbnail Available
    Item
    Comparative Study between Optimal Homotopy Asymptotic Method and Perturbation-Iteration Technique for Different Types of Nonlinear Equations
    (SPRINGER INTERNATIONAL PUBLISHING AG) Bildik, N; Deniz, S
    In this paper, we compare optimal homotopy asymptotic method and perturbation-iteration method to solve random nonlinear differential equations. Both of these methods are known to be new and very powerful for solving differential equations. We give some numerical examples to prove these claims. These illustrations are also used to check the convergence of the proposed methods.
  • No Thumbnail Available
    Item
    A new efficient method for solving delay differential equations and a comparison with other methods
    (SPRINGER HEIDELBERG) Bildik, N; Deniz, S
    In this paper, a new analytical technique, namely the optimal perturbation iteration method, is presented and applied to delay differential equations to find an efficient algorithm for their approximate solutions. Effectiveness of this method is tested by various examples of linear and nonlinear problems of delay differential equations. Obtained results reveal that optimal perturbation iteration algorithm is very effective, easy to use and simple to perform.