Miskolc mathematical notes/Mathematical notes · 2019 · 16 citations · 20 references
Natural SciencesElectrical EngineeringCircuit TheoryComputational PhysicsDifferential EquationsConvergence AnalysisFinite Difference MethodsNumerical Methods For Differential EquationsPerturbation MethodsSingular Perturbation TheoryTime IntegrationBoundary Layer BehaviorConvergence Under Mesh RefinementDelay Differential Equations With Singular PerturbationsMesh ConvergenceMesh Convergence AnalysisNonuniform Mesh TechniquesVolterra EquationsVolterra Integral Equations
In this paper, we analyze the convergence of the fitted mesh method applied to singularly perturbed Volterra delay-integro-differential equation. Our mesh comprises a special nonuniform mesh on the first subinterval and uniform mesh on another part. Error estimates are obtained using difference analogue of Gronwall's inequality with delay. A numerical test that confirms the theoretical results is presented.
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