scholarly journals The B-spline Collocation Approach for Coupled Klein-Gordon Equation

2019 ◽  
Author(s):  
Berat Karaagac
Keyword(s):  
Gordon Equation ◽  
Spline Collocation ◽  
B Spline ◽  
Klein Gordon ◽  
Collocation Approach ◽  
Klein Gordon Equation

scholarly journals Trigonometric Cubic B-spline Collocation Method for Solitons of the Klein-Gordon Equation

2016 ◽  
Author(s):  
Alper Korkmaz ◽  
Ozlem Ersoy ◽  
Idiris Dag
Keyword(s):  
Gordon Equation ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Coupled System ◽  
Initial Boundary ◽  
Spline Collocation ◽  
B Spline ◽  
Klein Gordon ◽  
Initial Boundary Value ◽  
Klein Gordon Equation

In the present study, we derive a new B-spline technique namely trigonometric B-spline collocation algorithm to solve some initial boundary value problems for the nonlinear Klein-Gordon equation. In order to carry out the time integration with Crank-Nicolson implicit method, the order of the equation is reduced to give a coupled system of nonlinear partial differential equations. The collocation approximation based on trigonometric cubic B-splines for spatial discretization is followed by the linearization of the nonlinear term. The efficiency and accuracy of the present method are validated by measuring the error between the numerical and analytical solutions when exist. The conservation laws representing momentum and energy are also computed for all problems.

scholarly journals Application of Hybrid Cubic B-Spline Collocation Approach for Solving a Generalized Nonlinear Klien-Gordon Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shazalina Mat Zin ◽  
Ahmad Abd Majid ◽  
Ahmad Izani Md. Ismail ◽  
Muhammad Abbas
Keyword(s):  
Approximate Solution ◽  
Space Dimension ◽  
Gordon Equation ◽  
Time Derivative ◽  
Test Problems ◽  
Spline Collocation ◽  
B Spline ◽  
Implicit Approach ◽  
Collocation Approach ◽  
Good Agreement

The generalized nonlinear Klien-Gordon equation is important in quantum mechanics and related fields. In this paper, a semi-implicit approach based on hybrid cubic B-spline is presented for the approximate solution of the nonlinear Klien-Gordon equation. The usual finite difference approach is used to discretize the time derivative while hybrid cubic B-spline is applied as an interpolating function in the space dimension. The results of applications to several test problems indicate good agreement with known solutions.

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

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040039 ◽  
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.

scholarly journals Fractional Klein-Gordon equation with singular mass

2021 ◽  
Vol 143 ◽  
pp. 110579
Author(s):  
Arshyn Altybay ◽  
Michael Ruzhansky ◽  
Mohammed Elamine Sebih ◽  
Niyaz Tokmagambetov
Keyword(s):  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation
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