Abstract
PurposeThe purpose of this study is to develop stable, convergent and accurate numerical method for solving singularly perturbed differential equations having both small and large delay.Design/methodology/approachThis study introduces a fitted nonpolynomial spline method for singularly perturbed differential equations having both small and large delay. The numerical scheme is developed on uniform mesh using fitted operator in the given differential equation.FindingsThe stability of the developed numerical method is established and its uniform convergence is proved. To validate the applicability of the method, one model problem is considered for numerical experimentation for different values of the perturbation parameter and mesh points.Originality/valueIn this paper, the authors consider a new governing problem having both small delay on convection term and large delay. As far as the researchers' knowledge is considered numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered.
Highlights
A differential equation is said to be singularly perturbed delay differential equation, if it includes at least one delay term, involving unknown functions occurring with different arguments, and the highest derivative term is multiplied by a small parameter
Consider the model singularly perturbed boundary value problem: −εy00ðxÞ þ 10y0ðxÞ À yðx À 1Þ þ y0ðx À εÞ 1⁄4 x x ∈ ð0; 1Þ ∪ ð1; 2Þ; Subject to the boundary conditions yðxÞ 1⁄4 1; x ∈ 1⁄2−1; 0; yð2Þ 1⁄4 2: 7. Discussion and conclusion This study introduces a fitted nonpolynomial spline method for singularly perturbed differential equations having both small and large delay
The numerical scheme is developed on uniform mesh using fitted operator in the given differential equation
Summary
A differential equation is said to be singularly perturbed delay differential equation, if it includes at least one delay term, involving unknown functions occurring with different arguments, and the highest derivative term is multiplied by a small parameter. AJMS authors of [5,6,7] have developed various numerical schemes on uniform meshes for singularly perturbed second-order differential equations having small delay on convection term. The purpose of this study is to develop stable, convergent and accurate numerical method for solving singularly perturbed differential-difference equations having both small and large delay. L1 and L2 are the linear operator associated to the domain Ω1 and Ω2, respectively
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