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- Title
A spectral shifted gegenbauer collocation method for fractional pantograph partial differential equations and its error analysis.
- Authors
Yaghoubi, S; Aminikhah, H; Sadri, K
- Abstract
This study presents a new numerical approach for solving fractional-order pantograph partial-differential equations, in which the fractional derivatives are expressed in the Caputo sense. New operational matrices are obtained by introducing the two-variable Gegenbauer polynomials. Using these matrices with the collocation method, solving the fractional order pantograph partial differential equation is converted into solving a system of algebraic equations. An error bound is computed for this method. Also, some examples are presented that show our proposed method has a better agreement with the exact solution in comparison with methods such as the homotopy perturbation and natural decomposition methods so that we can say that it is about 10 3 times more precise than the two mentioned methods. In general, our method provides a useful tool for solving these equations.
- Subjects
COLLOCATION methods; PANTOGRAPH; ALGEBRAIC equations; GEGENBAUER polynomials; MATRICES (Mathematics)
- Publication
Sādhanā: Academy Proceedings in Engineering Sciences, 2023, Vol 48, Issue 4, p1
- ISSN
0256-2499
- Publication type
Article
- DOI
10.1007/s12046-023-02270-5