TY - JOUR
ID - 39980
TI - Exponentially fitted tension spline method for singularly perturbed differential difference equations
JO - Iranian Journal of Numerical Analysis and Optimization
JA - IJNAO
LA - en
SN - 2423-6977
AU - Woldaregay, M.M.
AU - Duressa, G.F.
AD - Department of Applied athematics, Adama Science and Technology University, Adama, Ethiopia.
AD - Department of Mathematics, Jimma University, Jimma, Ethiopia.
Y1 - 2021
PY - 2021
VL - 11
IS - 2
SP - 261
EP - 282
KW - Differential difference
KW - Exponentially fitted
KW - Singularly perturbed problem
KW - Tension spline
KW - Uniform convergence
DO - 10.22067/ijnao.2021.68227.1009
N2 - In this article, singularly perturbed differential difference equations having delay and advance in the reaction terms are considered. The highest-order derivative term of the equation is multiplied by a perturbation parameter ε taking arbitrary values in the interval (0, 1]. For the small value of ε, the solution of the equation exhibits a boundary layer on the left or right side of the domain depending on the sign of the convective term. The terms with the shifts are approximated by using the Taylor series approximation.The resulting singularly perturbed boundary value problem is solved using an exponentially fitted tension spline method. The stability and uniform convergence of the scheme are discussed and proved. Numerical exam ples are considered for validating the theoretical analysis of the scheme. The developed scheme gives an accurate result with linear order uniform convergence.
UR - https://ijnao.um.ac.ir/article_39980.html
L1 - https://ijnao.um.ac.ir/article_39980_58f60f6fa77b8533e55d358295f5f824.pdf
ER -