Journal
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
Volume 33, Issue 4, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129183122500498
Keywords
Fibonacci polynomials; Chebyshev polynomials; fractional differential equations; spectral method; connection coefficients; operational matrix
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This paper focuses on developing spectral solutions for the nonlinear fractional Klein-Gordon equation. The typical collocation method and the tau method are used, along with a new operational matrix of fractional derivatives of Fibonacci polynomials. The resulting system of algebraic equations is solved to obtain a semi-analytic solution, and convergence and error analysis are discussed.
This paper is devoted to developing spectral solutions for the nonlinear fractional Klein-Gordon equation. The typical collocation method and the tau method are employed for obtaining the desired numerical solutions. In order to do this, a new operational matrix of fractional derivatives of Fibonacci polynomials is established. The idea behind the derivation of this matrix is based on utilizing the connection formula between the Fibonacci and Chebyshev polynomials. The introduced operational matrix is used along with the weighted residual quadrature spectral method and the collocation method to convert the nonlinear fractional Klein-Gordon equation into a system of algebraic equations. By solving the resulting system, we obtain a semi-analytic solution. The convergence and error analysis of the method are discussed. Some numerical results and discussions are presented aiming to illustrate the wide applicability and accuracy of the proposed algorithms.
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