2012
DOI: 10.1155/2012/579431
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Numerical Treatment of Singularly Perturbed Two‐Point Boundary Value Problems by Using Differential Transformation Method

Abstract: Differential transform method is adopted, for the first time, for solving linear singularly perturbed two-point boundary value problems. Four numerical examples are given to demonstrate the effectiveness of the present method. Results show that the numerical scheme is very effective and convenient for solving a large number of linear singularly perturbed two-point boundary value problems with high accuracy.

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Cited by 16 publications
(10 citation statements)
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“…In solving both ordinary differential equations and partial differential equations of various forms including integro-differential equations encountered in finance [26], the fractional type ordinary differential equation in [27]; the relatively new semi-analytical method known as differential transform method (DTM) is shown to be effective, reliable and easier in application when compared to other semi-analytical methods [28,29], even when the results agree.…”
Section: T DX T G T X T Dt G T X T Dw T Rmentioning
confidence: 99%
“…In solving both ordinary differential equations and partial differential equations of various forms including integro-differential equations encountered in finance [26], the fractional type ordinary differential equation in [27]; the relatively new semi-analytical method known as differential transform method (DTM) is shown to be effective, reliable and easier in application when compared to other semi-analytical methods [28,29], even when the results agree.…”
Section: T DX T G T X T Dt G T X T Dw T Rmentioning
confidence: 99%
“…For example Laplace is the integral transform used to find the solution of differential equations. Following transformation methods are reported in literature to find the solution of SPDE: Dogan et al [19] in 2012 numerically treated singularly perturbed two point boundary value problem using differential transformation method. This method is an iterative method for procuring analytical Taylor series solutions of differential equations and it can be used to solve both linear and nonlinear initial value problems.…”
Section: Transformation Methodsmentioning
confidence: 99%
“…A basic feature of regular perturbation problems is that the exact solution for small but nonzero ε smoothly approaches the unperturbed solution as ε ⟶ 0. A singular perturbation problem is defined as the one whose solution for ε � 0 is fundamentally different in character from the "neighbouring" solutions obtained in the limit ε ⟶ 0 [53,[55][56][57][58][59][60][61][62][63][64].…”
Section: Solving Complex Sp Nonlinear Problems: Recent Advances On Spmentioning
confidence: 99%