Numerical solution of a nonlinear Klein-Gordon equation

In this paper, we apply two decomposition methods, the Adomian decomposition method (ADM) and a well-established iterative method, to solve time-fractional Klein–Gordon type equation. We compare these methods and discuss the convergence of them. The obtained results reveal that these methods are very accurate and effective.

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A New Approach to Numerical Solution of Nonlinear Klein-Gordon Equation

Mathematical Problems in Engineering ◽

10.1155/2013/869749 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 14

Author(s):

Berna Bülbül ◽

Mehmet Sezer

Keyword(s):

Exact Solutions ◽

Numerical Solution ◽

Numerical Method ◽

Error Estimation ◽

Matrix Method ◽

Gordon Equation ◽

New Approach ◽

Collocation Points ◽

Klein Gordon ◽

Klein Gordon Equation

A numerical method based on collocation points is developed to solve the nonlinear Klein-Gordon equations by using the Taylor matrix method. The method is applied to some test examples and the numerical results are compared with the exact solutions. The results reveal that the method is very effective, simple, and convenient. In addition, an error estimation of proposed method is presented.

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On the numerical solution of the Klein-Gordon equation

Numerical Methods for Partial Differential Equations ◽

10.1002/num.20383 ◽

2009 ◽

Vol 25 (4) ◽

pp. 939-951 ◽

Cited By ~ 28

Author(s):

A.G. Bratsos

Keyword(s):

Numerical Solution ◽

Gordon Equation ◽

Klein Gordon ◽

Klein Gordon Equation

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DEVELOPMENT AND ANALYSIS OF NEW APPROXIMATION OF EXTENDED CUBIC B-SPLINE TO THE NONLINEAR TIME FRACTIONAL KLEIN–GORDON EQUATION

Fractals ◽

10.1142/s0218348x20400393 ◽

2020 ◽

Vol 28 (08) ◽

pp. 2040039 ◽

Cited By ~ 1

Author(s):

TAYYABA AKRAM ◽

MUHAMMAD ABBAS ◽

MUHAMMAD BILAL RIAZ ◽

AHMAD IZANI ISMAIL ◽

NORHASHIDAH MOHD. ALI

Keyword(s):

Fractional Derivative ◽

Numerical Solution ◽

Gordon Equation ◽

Basis Functions ◽

Unconditionally Stable ◽

B Spline ◽

Numerical Examples ◽

Caputo’S Fractional Derivative ◽

Klein Gordon ◽

Klein Gordon Equation

A new extended cubic B-spline (ECBS) approximation is formulated, analyzed and applied to obtain the numerical solution of the time fractional Klein–Gordon equation. The temporal fractional derivative is estimated using Caputo’s discretization and the space derivative is discretized by ECBS basis functions. A combination of Caputo’s fractional derivative and the new approximation of ECBS together with [Formula: see text]-weighted scheme is utilized to obtain the solution. The method is shown to be unconditionally stable and convergent. Numerical examples indicate that the obtained results compare well with other numerical results available in the literature.

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