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Accurate splitting approach to characterize the solution set of boundary layer problems | ||
| Computational Methods for Differential Equations | ||
| مقاله 5، دوره 7، شماره 2، تابستان 2019، صفحه 206-223 اصل مقاله (199.73 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
Khosro Sayevand  1؛ Jose Antonio Tenreiro Machado2
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| 1Faculty of Mathematical Sciences, Malayer University, P. O. Box 16846-13114, Malayer, Iran | ||
| 2Institute of Engineering of Polytechnic of Porto, Department of Electrical Engineering, Porto, Portugal | ||
| چکیده | ||
| The boundary layer (BL) is an important concept and refers to the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. This paper studies singularly perturbed fractional differential equations where the fractional derivatives are defined in the Caputo sense. The solution of such equations, with appropriate boundary conditions, displays BL behavior. The solution out of the BL is estimated by the solution of the reduced problem and the layer solution is approximated by means of a modified truncated Chebyshev series. The coefficients of the truncated series are evaluated using a novel operational matrix technique. Moreover, the stability and the error analysis of the proposed method are analyzed. Several examples illustrate the validity and applicability of the method. | ||
| کلیدواژهها | ||
| Singular perturbation؛ Boundary value problem؛ Shifted Chebyshev polynomial؛ Operational matrix؛ Boundary laye | ||
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