New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds
This paper is concerned with introducing two wavelets collocation algorithms for solving linear and nonlinear multipoint boundary value problems. The principal idea for obtaining spectral numerical solutions for such equations is employing third- and fourth-kind Chebyshev wavelets along with the spe...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/542839 |
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| _version_ | 1832565131513430016 |
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| author | W. M. Abd-Elhameed E. H. Doha Y. H. Youssri |
| author_facet | W. M. Abd-Elhameed E. H. Doha Y. H. Youssri |
| author_sort | W. M. Abd-Elhameed |
| collection | DOAJ |
| description | This paper is concerned with introducing two wavelets collocation algorithms for solving linear and nonlinear multipoint boundary value problems. The principal idea for obtaining spectral numerical solutions for such equations is employing third- and fourth-kind Chebyshev wavelets along with the spectral collocation method to transform the differential equation with its boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients which can be efficiently solved. Convergence analysis and some specific numerical examples are discussed to demonstrate the validity and applicability of the proposed algorithms. The obtained numerical results are comparing favorably
with the analytical known solutions. |
| format | Article |
| id | doaj-art-db6616a4b4c94989916501c4b52f3f19 |
| 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-db6616a4b4c94989916501c4b52f3f192025-02-03T01:09:23ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/542839542839New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth KindsW. M. Abd-Elhameed0E. H. Doha1Y. H. Youssri2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptThis paper is concerned with introducing two wavelets collocation algorithms for solving linear and nonlinear multipoint boundary value problems. The principal idea for obtaining spectral numerical solutions for such equations is employing third- and fourth-kind Chebyshev wavelets along with the spectral collocation method to transform the differential equation with its boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients which can be efficiently solved. Convergence analysis and some specific numerical examples are discussed to demonstrate the validity and applicability of the proposed algorithms. The obtained numerical results are comparing favorably with the analytical known solutions.http://dx.doi.org/10.1155/2013/542839 |
| spellingShingle | W. M. Abd-Elhameed E. H. Doha Y. H. Youssri New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds Abstract and Applied Analysis |
| title | New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds |
| title_full | New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds |
| title_fullStr | New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds |
| title_full_unstemmed | New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds |
| title_short | New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds |
| title_sort | new wavelets collocation method for solving second order multipoint boundary value problems using chebyshev polynomials of third and fourth kinds |
| url | http://dx.doi.org/10.1155/2013/542839 |
| work_keys_str_mv | AT wmabdelhameed newwaveletscollocationmethodforsolvingsecondordermultipointboundaryvalueproblemsusingchebyshevpolynomialsofthirdandfourthkinds AT ehdoha newwaveletscollocationmethodforsolvingsecondordermultipointboundaryvalueproblemsusingchebyshevpolynomialsofthirdandfourthkinds AT yhyoussri newwaveletscollocationmethodforsolvingsecondordermultipointboundaryvalueproblemsusingchebyshevpolynomialsofthirdandfourthkinds |