Abstract and Applied Analysis

New Ultraspherical Wavelets Spectral Solutions for Fractional Riccati Differential Equations

W. M. Abd-Elhameed and Y. H. Youssri

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Abstract

We introduce two new spectral wavelets algorithms for solving linear and nonlinear fractional-order Riccati differential equation. The suggested algorithms are basically based on employing the ultraspherical wavelets together with the tau and collocation spectral methods. The main idea for obtaining spectral numerical solutions depends on converting the differential equation with its initial condition into a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. For the sake of illustrating the efficiency and the applicability of our algorithms, some numerical examples including comparisons with some algorithms in the literature are presented.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 626275, 8 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607129

Digital Object Identifier
doi:10.1155/2014/626275

Mathematical Reviews number (MathSciNet)
MR3214442

Zentralblatt MATH identifier
07022761

Citation

Abd-Elhameed, W. M.; Youssri, Y. H. New Ultraspherical Wavelets Spectral Solutions for Fractional Riccati Differential Equations. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 626275, 8 pages. doi:10.1155/2014/626275. https://projecteuclid.org/euclid.aaa/1412607129


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