A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations
Fevzi Erdoğan, Mehmet Giyas Sakar, Onur Saldır
Abstract
Abstract The purpose of this paper is to present a uniform finite difference method for numerical solution of a initial value problem for semilinear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method is shown to uniformly convergent with respect to the perturbation parameter. A numerical experiment illustrate in practice the result of convergence proved theoretically.
Topics & Concepts
MathematicsPiecewiseUniform convergenceSingular perturbationFinite difference methodMathematical analysisConvergence (economics)Finite differencePerturbation (astronomy)Differential equationNumerical analysisApplied mathematicsComputer sciencePhysicsEconomic growthEconomicsQuantum mechanicsComputer networkBandwidth (computing)Differential Equations and Numerical MethodsAdvanced Mathematical Modeling in EngineeringDifferential Equations and Boundary Problems