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Abbasbandy, Saeid, Sahihi, Hussein, Allahviranloo, Tofigh. (1401). Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems. سامانه مدیریت نشریات علمی, 10(4), 942-953. doi: 10.22034/cmde.2021.40288.1758
Saeid Abbasbandy; Hussein Sahihi; Tofigh Allahviranloo. "Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems". سامانه مدیریت نشریات علمی, 10, 4, 1401, 942-953. doi: 10.22034/cmde.2021.40288.1758
Abbasbandy, Saeid, Sahihi, Hussein, Allahviranloo, Tofigh. (1401). 'Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems', سامانه مدیریت نشریات علمی, 10(4), pp. 942-953. doi: 10.22034/cmde.2021.40288.1758
Abbasbandy, Saeid, Sahihi, Hussein, Allahviranloo, Tofigh. Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems. سامانه مدیریت نشریات علمی, 1401; 10(4): 942-953. doi: 10.22034/cmde.2021.40288.1758

Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems

Computational Methods for Differential Equations
مقاله 8، دوره 10، شماره 4، دی 2022، صفحه 942-953    اصل مقاله (611.92 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.40288.1758
نویسندگان
Saeid Abbasbandy* 1؛ Hussein Sahihi2؛ Tofigh Allahviranloo3
1Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34149-16818, Iran.
2Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
3Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey.
چکیده
In this paper, a reliable new scheme is presented based on combining Reproducing Kernel Method (RKM) with a practical technique for the nonlinear problem to solve the System of Singularly Perturbed Boundary Value Problems (SSPBVP). The Gram-Schmidt orthogonalization process is removed in the present RKM. However, we provide error estimation for the approximate solution and its derivative. Based on the present algorithm in this paper, can also solve linear problem. Several numerical examples demonstrate that the present algorithm does have higher precision. 
کلیدواژه‌ها
Reproducing kernel method؛ Singularly perturbed BVPs؛ Convergence analysis؛ Error analysis؛ System of differential equations
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