Advances in Difference Equations · 2014 · 34 citations · 21 references
Natural SciencesPhysicsDifferential EquationsConvergence AnalysisFinite Difference MethodsNumerical AnalysisNumerical ConvergenceNumerical Methods For Differential EquationsPerturbation TheoryConvergenceDiscrete Maximum PrincipleFinite Difference SchemesMesh ConvergenceSingular Perturbation AnalysisStability Of Numerical SchemesVolterra EquationsVolterra Integral Equations
We study the convergence properties of a difference scheme for singularly perturbed Volterra integro-differential equations on a graded mesh. We show that the scheme is first-order convergent in the discrete maximum norm, independently of the perturbation parameter. Numerical experiments are presented, which are in agreement with the theoretical results.
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Differential and Integral Calculus.
Louis Brand, R. Courant, E. J. McShane · American Mathematical Monthly · 1935 · 162 citations