Solving a class of variable-order differential equations via Ritz-approximation method and Genocchi polynomials
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.
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.
Keywords
Ritz-approximation; Caputo variable-order derivative; Genocchi polynomials; satisfier function
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