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Sharifi, Shokofeh, Jalil, Rashidinia. (1397). An ${\cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems. فیزیولوژی و بیوتکنولوژی آبزیان, 6(1), 27-46. doi: 10.22124/jmm.2018.2761
Shokofeh Sharifi; Rashidinia Jalil. "An ${\cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems". فیزیولوژی و بیوتکنولوژی آبزیان, 6, 1, 1397, 27-46. doi: 10.22124/jmm.2018.2761
Sharifi, Shokofeh, Jalil, Rashidinia. (1397). 'An ${\cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems', فیزیولوژی و بیوتکنولوژی آبزیان, 6(1), pp. 27-46. doi: 10.22124/jmm.2018.2761
Sharifi, Shokofeh, Jalil, Rashidinia. An ${\cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems. فیزیولوژی و بیوتکنولوژی آبزیان, 1397; 6(1): 27-46. doi: 10.22124/jmm.2018.2761

An ${\cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems

Journal of Mathematical Modeling
مقاله 2، دوره 6، شماره 1، مهر 2018، صفحه 27-46    اصل مقاله (236.32 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2018.2761
نویسندگان
Shokofeh Sharifi1؛ Rashidinia Jalil* 2
1Department of Mathematics and statistics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
چکیده
As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only ${\cal O}(h^{2})$ accuracy and this approximation is non-optimal. In this work, we obtain an optimal spline collocation method for solving the general nonlinear seventh order two points boundary value problems. The ${\cal O}(h^{8})$ convergence analysis, mainly based on the Green's function approach, has been proved. Numerical illustration demonstrate the applicability of the purposed method. Three test problems have been solved and the computed results have been compared with the results obtained by recent existing methods to verify the accurate nature of our method.
کلیدواژه‌ها
Nonlinear boundary value problems؛ eighth degree B-spline؛ collocation method؛ convergence Analysis؛ Green's function
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