Solving a class of variable-order differential equations via Ritz-approximation method and Genocchi polynomials

Authors

  • Somayeh Sheykhi University of Mazandaran
  • Mashaallah Matinfar Associate professor of University of Mazandaran
  • Mohammad Arab Firoozjaee Assistant Professor of University of Science and Technology of Mazandaran

Keywords:

Ritz-approximation, Caputo variable-order derivative, Genocchi polynomials, satisfier function

Abstract

In this article, a class of variable-order differential equations
by the Ritz-approximation is solved. Firstly, the unknown function is
estimated using the Ritz-approximation via Genocchi polynomials as
the basis functions. Then, by collocation method and preference of
Genocchi roots as the collocation points, a set of algebraic equations is
obtained. This system of nonlinear equations is solved by Mathematica
10 software. Finally, by solving some numerical examples and comparing the achieved results with other methods, the validity and efficiency
of the presented method are shown.

Author Biographies

Mashaallah Matinfar, Associate professor of University of Mazandaran

Department of Mathematics, University of Mazandaran

Mohammad Arab Firoozjaee, Assistant Professor of University of Science and Technology of Mazandaran

Department of Mathematics, University of Science and Technology of Mazandaran

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Published

2022-01-20

Issue

Vol. 15

Section

Vol. 15, No. 5, (2021)

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