Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations
We extend a collocation method for solving a nonlinear ordinary differential equation (ODE) via Jacobi polynomials. To date, researchers usually use Chebyshev or Legendre collocation method for solving problems in chemistry, physics, and so forth, see the wor...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/673085 |
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| _version_ | 1850220853354037248 |
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| author | Ahmad Imani Azim Aminataei Ali Imani |
| author_facet | Ahmad Imani Azim Aminataei Ali Imani |
| author_sort | Ahmad Imani |
| collection | DOAJ |
| description | We extend a
collocation method for solving a nonlinear
ordinary differential
equation (ODE) via Jacobi polynomials. To date, researchers
usually use Chebyshev or Legendre collocation method for solving
problems in chemistry, physics, and so forth, see the works of (Doha and Bhrawy 2006, Guo 2000, and Guo et al. 2002). Choosing the optimal polynomial for solving every ODEs problem
depends on many factors, for example, smoothing continuously and
other properties of the solutions. In this paper, we show
intuitionally that in some problems choosing other members of
Jacobi polynomials gives better result compared to Chebyshev or
Legendre polynomials. |
| format | Article |
| id | doaj-art-7bca4c487c3e4b0591313f01e685866d |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7bca4c487c3e4b0591313f01e685866d2025-08-20T02:06:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/673085673085Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential EquationsAhmad Imani0Azim Aminataei1Ali Imani2Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-175, Tehran, IranDepartment of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran 1541849611, IranDepartment of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran 1541849611, IranWe extend a collocation method for solving a nonlinear ordinary differential equation (ODE) via Jacobi polynomials. To date, researchers usually use Chebyshev or Legendre collocation method for solving problems in chemistry, physics, and so forth, see the works of (Doha and Bhrawy 2006, Guo 2000, and Guo et al. 2002). Choosing the optimal polynomial for solving every ODEs problem depends on many factors, for example, smoothing continuously and other properties of the solutions. In this paper, we show intuitionally that in some problems choosing other members of Jacobi polynomials gives better result compared to Chebyshev or Legendre polynomials.http://dx.doi.org/10.1155/2011/673085 |
| spellingShingle | Ahmad Imani Azim Aminataei Ali Imani Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations International Journal of Mathematics and Mathematical Sciences |
| title | Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations |
| title_full | Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations |
| title_fullStr | Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations |
| title_full_unstemmed | Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations |
| title_short | Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations |
| title_sort | collocation method via jacobi polynomials for solving nonlinear ordinary differential equations |
| url | http://dx.doi.org/10.1155/2011/673085 |
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