A second order numerical method for singularly perturbed Volterra integro-differential equations with delay
Fevzi Erdoğan
Abstract
Abstract This study deals with singularly perturbed Volterra integro-differential equations with delay. Based on the properties of the exact solution, a hybrid difference scheme with appropriate quadrature rules on a Shishkin-type mesh is constructed. By using the truncation error estimate techniques and a discrete analogue of Grönwall’s inequality it is proved that the hybrid finite difference scheme is almost second order accurate in the discrete maximum norm. Numerical experiments support these theoretical results and indicate that the estimates are sharp.
Topics & Concepts
MathematicsQuadrature (astronomy)Differential equationNumerical analysisApplied mathematicsNorm (philosophy)Finite difference methodMathematical analysisOrder (exchange)LawElectrical engineeringPolitical scienceFinanceEconomicsEngineeringDifferential Equations and Numerical MethodsNumerical methods for differential equationsDifferential Equations and Boundary Problems