scholarly journals The numerical solution of the time-fractional non-linear Klein-Gordon equation via spectral collocation method

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1529-1537 ◽  
Author(s):  
Yin Yang ◽  
Xinfa Yang ◽  
Jindi Wang ◽  
Jie Liu
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Gordon Equation ◽  
Spectral Expansion ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
L2 Norm ◽  
Non Linear ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper, we consider the numerical solution of the time-fractional non-linear Klein-Gordon equation. We propose a spectral collocation method in both temporal and spatial discretizations with a spectral expansion of Jacobi interpolation polynomial for this equation. A rigorous error analysis is provided for the spectral methods to show both the errors of approximate solutions and the errors of approximate derivatives of the solutions decaying exponentially in infinity-norm and weighted L2-norm. Numerical tests are carried out to confirm the theoretical results.

scholarly journals Space–time spectral collocation method for Klein–Gordon equation

2021 ◽  
Vol 15 ◽  
pp. 174830262110653
Author(s):  
Ping Zhang ◽  
Te Li ◽  
Yuan-Hao Zhang
Keyword(s):  
Collocation Method ◽  
Iterative Algorithm ◽  
Lagrange Interpolation ◽  
High Efficiency ◽  
Gordon Equation ◽  
Laguerre Function ◽  
Spectral Collocation ◽  
Klein Gordon ◽  
Collocation Scheme ◽  
Klein Gordon Equation

By using the Legendre–Laguerre collocation method, we can construct a spectral collocation scheme to solve the Klein–Gordon equation on the half-line. The Laguerre function collocation method (based on the Lagrange interpolation) in space and the Legendre–Gauss–Lobatto collocation method in time are used. A Newton iterative algorithm is provided. The numerical results demonstrate the high efficiency and accuracy of suggested algorithms.

A Bohmian approach to the perturbations of non-linear Klein–Gordon equation

Pramana ◽  
2016 ◽  
Vol 87 (2) ◽  
Author(s):  
FARAMARZ RAHMANI ◽  
MEHDI GOLSHANI ◽  
MOHSEN SARBISHEI
Keyword(s):  
Gordon Equation ◽  
Non Linear ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Numerical study of heat transfer of a micropolar fluid through a porous medium with radiation

2018 ◽  
Vol 22 (1 Part B) ◽  
pp. 557-565 ◽  
Author(s):  
Fakhrodin Mohammadi ◽  
Mohammad Rashidi
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Collocation Method ◽  
Micropolar Fluid ◽  
Legendre Polynomials ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Shifted Legendre Polynomials ◽  
Non Linear

An efficient Spectral Collocation method based on the shifted Legendre polynomials was applied to get solution of heat transfer of a micropolar fluid through a porous medium with radiation. A similarity transformation is applied to convert the governing equations to a system of non-linear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of derivative are used for producing an approximate solution for this system of non-linear differential equations. The main advantage of the proposed method is that the need for guessing and correcting the initial values during the solution procedure is eliminated and a stable solution with good accuracy can be obtained by using the given boundary conditions in the problem. A very good agreement is observed between the obtained results by the proposed Spectral Collocation method and those of previously published ones.

Sign in / Sign up

Export Citation Format

Share Document