TY - JOUR
ID - 8666
TI - Accurate splitting approach to characterize the solution set of boundary layer problems
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Sayevand, Khosro
AU - Tenreiro Machado, Jose Antonio
AD - Faculty of Mathematical Sciences, Malayer University,
P. O. Box 16846-13114, Malayer, Iran
AD - Institute of Engineering of Polytechnic of Porto,
Department of Electrical Engineering, Porto, Portugal
Y1 - 2019
PY - 2019
VL - 7
IS - 2
SP - 206
EP - 223
KW - Singular perturbation
KW - Boundary value problem
KW - Shifted Chebyshev polynomial
KW - Operational matrix
KW - Boundary laye
DO -
N2 - 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.
UR - https://cmde.tabrizu.ac.ir/article_8666.html
L1 - https://cmde.tabrizu.ac.ir/article_8666_d7b613d4c647b73430148d5432da5c39.pdf
ER -