A numerical solution of the generalized Burger’s–Huxley equation by spectral collocation method

2006 ◽  
Vol 178 (2) ◽  
pp. 338-344 ◽  
Author(s):  
M. Javidi
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Huxley Equation

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.

Numerical Solution of Electrodynamic Flow by Using Pseudo-spectral Collocation Method

2013 ◽  
Vol 41 (1) ◽  
pp. 43-49
Author(s):  
Davood Rostamy ◽  
Kobra Karimi ◽  
Fateme Zabihi ◽  
Mohsen Alipour
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Pseudo Spectral

SPECTRAL COLLOCATION METHOD FOR MULTI-ORDER FRACTIONAL DIFFERENTIAL EQUATIONS

2014 ◽  
Vol 11 (05) ◽  
pp. 1350072 ◽  
Author(s):  
F. GHOREISHI ◽  
P. MOKHTARY
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Fractional Differential Equations ◽  
Jacobi Polynomials ◽  
Transformation Method ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Fractional Differential ◽  
New Equation

In this paper, the spectral collocation method is investigated for the numerical solution of multi-order Fractional Differential Equations (FDEs). We choose the orthogonal Jacobi polynomials and set of Jacobi Gauss–Lobatto quadrature points as basis functions and grid points respectively. This solution strategy is an application of the matrix-vector-product approach in spectral approximation of FDEs. The fractional derivatives are described in the Caputo type. Numerical solvability and an efficient convergence analysis of the method have also been discussed. Due to the fact that the solutions of fractional differential equations usually have a weak singularity at origin, we use a variable transformation method to change some classes of the original equation into a new equation with a unique smooth solution such that, the spectral collocation method can be applied conveniently. We prove that after this regularization technique, numerical solution of the new equation has exponential rate of convergence. Some standard examples are provided to confirm the reliability of the proposed method.

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