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A deficient spline function approximation to fourth-order differential equations |
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| Authors: | M. Nabil EsmailTharwat Fawzy Magdy AhmedHamdi O. Elmoselhi |
| Affiliation: | Department of Chemical Engineering, University of Saskatchewan, Saskatoon, Canada Department of Mathematics, Faculty of Science, University of Suez Canal, Ismilia, Egypt Department of Science & Mathematics, Faculty of Petroleum and Mining, University of Suez Canal, Suez, Egypt |
| Abstract: | An approximate spline solution is developed for the initial value problem of a fourth-order ordinary differential equation. The approximation is based on deficient spline polynomials of degree M = 8 and deficiency 4. The existence and uniqueness of the solution, which satisfies a Lipschitz condition, are proved. The consistency, stability, and consequently convergence of the solution are established. Furthermore, the method is proved to be of order 9, and the errors are limited by the relation S(i)(x) − y(i)(x) = O(h9 − i), I = 0(1)8. |
| Keywords: | spline functions numerical solutions ordinary differential equations |
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