Abstract and Applied Analysis

A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain

Faezeh Toutounian, Emran Tohidi, and Stanford Shateyi

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Abstract

This paper contributes a new matrix method for the solution of high-order linear complex differential equations with variable coefficients in rectangular domains under the considered initial conditions. On the basis of the presented approach, the matrix forms of the Bernoulli polynomials and their derivatives are constructed, and then by substituting the collocation points into the matrix forms, the fundamental matrix equation is formed. This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown Bernoulli coefficients are determined and thus the approximate solutions are obtained. Also, an error analysis based on the use of the Bernoulli polynomials is provided under several mild conditions. To illustrate the efficiency of our method, some numerical examples are given.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 823098, 12 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511833

Digital Object Identifier
doi:10.1155/2013/823098

Mathematical Reviews number (MathSciNet)
MR3039185

Zentralblatt MATH identifier
1275.65041

Citation

Toutounian, Faezeh; Tohidi, Emran; Shateyi, Stanford. A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain. Abstr. Appl. Anal. 2013 (2013), Article ID 823098, 12 pages. doi:10.1155/2013/823098. https://projecteuclid.org/euclid.aaa/1393511833


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