TY - JOUR
ID - 57949
T1 - Accurate Numerical Method for Singularly Perturbed Differential-Difference Equations with Mixed Shifts
JO - Khayyam Journal of Mathematics
JA - KJM
LA - en
SN -
A1 - Kumara Swamy, Diddi
A1 - Phaneendra, Kolloju
A1 - Reddy, Y.N.
Y1 - 2018
PY - 2018/07/01
VL - 4
IS - 2
SP - 110
EP - 122
KW - Singularly perturbed differential-difference equation
KW - Fitting factor
KW - Boundary Layer
KW - Tridiagonal system
KW - Truncation error
DO - 10.22034/kjm.2018.57949
N2 - This paper is concerned with the numerical solution of the singularly perturbed differential-difference equations with small shifts called delay and advanced parameters. A fourth order finite difference method with a fitting factor is proposed for the solution of the singularly perturbed differential-difference equations with mixed shifts. The delay and advanced shifts are managed by Taylor series and an asymptotically equivalent singularly perturbed two-point boundary value problem is obtained. A fitting factor is introduced in the fourth order finite difference scheme for the problem which takes care of the small values of the perturbation parameter. This fitting factor is obtained from the asymptotic solution of singular perturbations. Thomas algorithm is used to solve the discrete system of the difference scheme. Convergence of the proposed method is analyzed. Maximum absolute errors in comparison with the several numerical experiments aretabulated to illustrate the proposed method.
UR - http://www.kjm-math.org/article_57949.html
L1 - http://www.kjm-math.org/pdf_57949_faad09b64d50416a8548558290d7ffba.html
ER -