A computational algorithm for simulating fractional order relaxation–oscillation equation

Autores: Mohammad Izadi
Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 79, Nº. 4, 2022, págs. 647-661
Idioma: inglés
DOI: 10.1007/s40324-021-00266-x
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Resumen
- In the present work, a collocation approach is developed to find an approximate solution of fractional relaxation-oscillation differential equation describing the processes of relaxation and oscillation in many physical systems. The method is relied on generalized Chebyshev polynomials as basis functions, collocation points, and the matrix operations. The proposed scheme converts the underlying fractional initial value problems into a matrix equation, which corresponds to a set of linear algebraic equations consist of polynomial coefficients. An error estimation based on residual function is performed to show the accuracy of the results. Hence, an improvement of the approximate solutions are obtained based upon this error estimation. To illustrate the utility and applicability of the technique, three numerical examples are given and the comparisons between the numerical results of the proposed method with existing results are carried out. The experiments show the accuracy and efficiency the present work.