Numerical Functional Analysis and Optimization · 2013 · 31 citations · 26 references
Natural SciencesMathematicsComputational PhysicsDifferential EquationsDynamical SystemsIntegral EquationsNumerical Methods For Differential EquationsSpectral AnalysisSpectral MethodsSpectral TheoryConvergenceNumerical Methods For Integral EquationsSpectral ApproximationSpectral ConvergenceVolterra EquationsVolterra Integral EquationsVolterra Theory
Abstract The main purpose of this work is to provide a numerical method for the solution of Volterra functional integro-differential equations of neutral type based on a spectral approach. We analyze the convergence properties of the spectral method to approximate smooth solutions of Volterra functional integro-differential equations of neutral type. It is shown that for the neutral integro-differential equations, the spectral methods yield an exponential order of convergence. Keywords: Delay differential equationError analysisNeutral equationsSpectral methodVolterra functional integro-differential equationMathematics Subject Classification: 45J0565M1265M70 Notes Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lnfa.
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