A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials
In this study, a novel matrix method based on collocation points is proposed to solve some linear and nonlinear integro-differential equations with variable coefficients under the mixed conditions. The solutions are obtained by means of Dickson and Taylor polynomials. The presented method transforms...
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2017
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my-ukm.journal.106872017-09-20T09:02:52Z http://journalarticle.ukm.my/10687/ A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials Kürkçü, Ömür Kivanç Aslan, Ersin Sezer, Mehmet In this study, a novel matrix method based on collocation points is proposed to solve some linear and nonlinear integro-differential equations with variable coefficients under the mixed conditions. The solutions are obtained by means of Dickson and Taylor polynomials. The presented method transforms the equation and its conditions into matrix equations which comply with a system of linear algebraic equations with unknown Dickson coefficients, via collocation points in a finite interval. While solving the matrix equation, the Dickson coefficients and the polynomial approximation are obtained. Besides, the residual error analysis for our method is presented and illustrative examples are given to demonstrate the validity and applicability of the method. Penerbit Universiti Kebangsaan Malaysia 2017-02 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/10687/1/19%20Omur%20Kivanc.pdf Kürkçü, Ömür Kivanç and Aslan, Ersin and Sezer, Mehmet (2017) A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials. Sains Malaysiana, 46 (2). pp. 335-347. ISSN 0126-6039 http://www.ukm.my/jsm/english_journals/vol46num2_2017/contentsVol46num2_2017.html |
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In this study, a novel matrix method based on collocation points is proposed to solve some linear and nonlinear integro-differential equations with variable coefficients under the mixed conditions. The solutions are obtained by means of Dickson and Taylor polynomials. The presented method transforms the equation and its conditions into matrix equations which comply with a system of linear algebraic equations with unknown Dickson coefficients, via collocation points in a finite interval. While solving the matrix equation, the Dickson coefficients and the polynomial approximation are obtained. Besides, the residual error analysis for our method is presented and illustrative examples are given to demonstrate the validity and applicability of the method. |
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Article |
author |
Kürkçü, Ömür Kivanç Aslan, Ersin Sezer, Mehmet |
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Kürkçü, Ömür Kivanç Aslan, Ersin Sezer, Mehmet A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials |
author_facet |
Kürkçü, Ömür Kivanç Aslan, Ersin Sezer, Mehmet |
author_sort |
Kürkçü, Ömür Kivanç |
title |
A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials |
title_short |
A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials |
title_full |
A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials |
title_fullStr |
A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials |
title_full_unstemmed |
A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials |
title_sort |
novel collocation method based on residual error analysis for solving integro-differential equations using hybrid dickson and taylor polynomials |
publisher |
Penerbit Universiti Kebangsaan Malaysia |
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2017 |
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http://journalarticle.ukm.my/10687/1/19%20Omur%20Kivanc.pdf http://journalarticle.ukm.my/10687/ http://www.ukm.my/jsm/english_journals/vol46num2_2017/contentsVol46num2_2017.html |
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