TY - JOUR
T1 - Approximate analytical solutions for singularly perturbed boundary value problems by multi-step differential transform method
AU - El-Zahar, Essam R.
PY - 2012
Y1 - 2012
N2 - In this study, a reliable algorithm to develop approximate solutions for two point singularly perturbed boundary value problems exhibiting boundary layers is proposed. Using singular perturbation analysis, the original problem is replaced by two suitable first order Initial Value Problems (IVPs). Then, the multi-step differential transform method is applied to solve these IVPs. Several illustrated examples of linear and nonlinear problems are given to demonstrate the effectiveness of the present method. Numerical results show that the present method is very effective and convenient for solving a large number of singularly perturbed problems with high accuracy.
AB - In this study, a reliable algorithm to develop approximate solutions for two point singularly perturbed boundary value problems exhibiting boundary layers is proposed. Using singular perturbation analysis, the original problem is replaced by two suitable first order Initial Value Problems (IVPs). Then, the multi-step differential transform method is applied to solve these IVPs. Several illustrated examples of linear and nonlinear problems are given to demonstrate the effectiveness of the present method. Numerical results show that the present method is very effective and convenient for solving a large number of singularly perturbed problems with high accuracy.
KW - Boundaq layer problems
KW - Differential tramform method multi-step dfferential tramform method
KW - Singular pedurbation problems
UR - http://www.scopus.com/inward/record.url?scp=84867280332&partnerID=8YFLogxK
U2 - 10.3923/jas.2012.2026.2034
DO - 10.3923/jas.2012.2026.2034
M3 - Article
AN - SCOPUS:84867280332
SN - 1812-5654
VL - 12
SP - 2026
EP - 2034
JO - Journal of Applied Sciences
JF - Journal of Applied Sciences
IS - 19
ER -