A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain
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 d...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/823098 |
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| author | Faezeh Toutounian Emran Tohidi Stanford Shateyi |
| author_facet | Faezeh Toutounian Emran Tohidi Stanford Shateyi |
| author_sort | Faezeh Toutounian |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-638f839f2df54ad3a79d55ed565874ab |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-638f839f2df54ad3a79d55ed565874ab2025-02-03T00:59:21ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/823098823098A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular DomainFaezeh Toutounian0Emran Tohidi1Stanford Shateyi2Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranDepartment of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranDepartment of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South AfricaThis 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.http://dx.doi.org/10.1155/2013/823098 |
| spellingShingle | Faezeh Toutounian Emran Tohidi Stanford Shateyi A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain Abstract and Applied Analysis |
| title | A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain |
| title_full | A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain |
| title_fullStr | A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain |
| title_full_unstemmed | A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain |
| title_short | A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain |
| title_sort | collocation method based on the bernoulli operational matrix for solving high order linear complex differential equations in a rectangular domain |
| url | http://dx.doi.org/10.1155/2013/823098 |
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