International journal of mathematics and computation · 2015 · 31 citations · 20 references
Natural SciencesComputational EngineeringComputational MechanicsDifferential EquationsConvergence AnalysisFinite Difference MethodsIntegral EquationsNumerical Methods For Differential EquationsPerturbation TheorySingular Perturbation TheoryBoundary Integral ConditionsConvergenceFinite Difference ApproximationFinite Difference DiscretizationFinite Difference SchemesMesh ConvergenceSingular Perturbations In Ordinary Differential EquationsUniform Convergence
Consider the singularly perturbed second order ordinary differential equation with integral boundary condition. Before presenting the numerical method for its solution necessary asymptotic bounds have been obtained. Uniform convergence of the approximate solution on an uniform mesh is proved. Numerical example supporting the theorical analysis is presented.
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