Mathematics of Computation · 1977 · 28 citations · 8 references
Natural SciencesElectrical EngineeringMathematicsComputational MechanicsComputational PhysicsDifferential EquationsConvergence AnalysisIntegral EquationsNumerical AlgorithmsNumerical ConvergenceNumerical IntegrationNumerical Methods For Differential EquationsAsymptotic AnalysisNumerical Integration Error AnalysisNumerical Methods For Integral EquationsTruncationTruncation ErrorTruncation Error AnalysisVolterra EquationsVolterra Integral Equations
Algorithms based on the use of Taylor series are developed for the numerical solution of Volterra integral and integro-differential equations of arbitrary order. It is shown that these algorithms are uniformly convergent, bounds are obtained for the truncation error, and an asymptotic error analysis is provided for the integral equation case. The various problems of computer implementation are discussed, and the results of certain experiments suggested by the theory are presented.
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