## Abstract and Applied Analysis

### Numerical Solutions of Odd Order Linear and Nonlinear Initial Value Problems Using a Shifted Jacobi Spectral Approximations

#### Abstract

A shifted Jacobi Galerkin method is introduced to get a direct solution technique for solving the third- and fifth-order differential equations with constant coefficients subject to initial conditions. The key to the efficiency of these algorithms is to construct appropriate base functions, which lead to systems with specially structured matrices that can be efficiently inverted. A quadrature Galerkin method is introduced for the numerical solution of these problems with variable coefficients. A new shifted Jacobi collocation method based on basis functions satisfying the initial conditions is presented for solving nonlinear initial value problems. Through several numerical examples, we evaluate the accuracy and performance of the proposed algorithms. The algorithms are easy to implement and yield very accurate results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 364360, 25 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.aaa/1355495862

Digital Object Identifier
doi:10.1155/2012/364360

Mathematical Reviews number (MathSciNet)
MR2970001

Zentralblatt MATH identifier
1253.65157

#### Citation

Bhrawy, A. H.; Alghamdi, M. A. Numerical Solutions of Odd Order Linear and Nonlinear Initial Value Problems Using a Shifted Jacobi Spectral Approximations. Abstr. Appl. Anal. 2012 (2012), Article ID 364360, 25 pages. doi:10.1155/2012/364360. https://projecteuclid.org/euclid.aaa/1355495862

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