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Khosro Sayevand

Academic rank: Professor
ORCID:
Education: PhD.
ScopusId:
HIndex:
Faculty: Mathematical Sciences and Statistics
Address: Malayer University
Phone: 081-33398981

Research

Title
Accurate splitting approach to characterize the solution set of bound- ary layer problems
Type
JournalPaper
Keywords
Singular perturbation, Boundary value problem, Shifted Chebyshev polynomial, Operational matrix, Boundary layer, Caputo fractional derivative.
Year
2019
Journal computational methods for differential equations
DOI
Researchers Khosro Sayevand

Abstract

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.