Numerical Solutions of Odd Order Linear and Nonlinear Initial Value Problems Using a Shifted Jacobi Spectral Approximations
Joint Authors
Bhrawy, Ali H.
Alghamdi, Mohammad Ali
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-25, 25 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-12
Country of Publication
Egypt
No. of Pages
25
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Bhrawy, Ali H.& Alghamdi, Mohammad Ali. 2012. Numerical Solutions of Odd Order Linear and Nonlinear Initial Value Problems Using a Shifted Jacobi Spectral Approximations. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-25.
https://search.emarefa.net/detail/BIM-466146
Modern Language Association (MLA)
Bhrawy, Ali H.& Alghamdi, Mohammad Ali. Numerical Solutions of Odd Order Linear and Nonlinear Initial Value Problems Using a Shifted Jacobi Spectral Approximations. Abstract and Applied Analysis No. 2012 (2012), pp.1-25.
https://search.emarefa.net/detail/BIM-466146
American Medical Association (AMA)
Bhrawy, Ali H.& Alghamdi, Mohammad Ali. Numerical Solutions of Odd Order Linear and Nonlinear Initial Value Problems Using a Shifted Jacobi Spectral Approximations. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-25.
https://search.emarefa.net/detail/BIM-466146
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-466146