Mathematics of Computation · 1988 · 47 citations · 18 references
Natural SciencesMathematicsDifferential EquationsDynamical SystemsConvergence AnalysisFinite Difference MethodsNumerical AnalysisNumerical ConvergenceNumerical Methods For Differential EquationsSystems Of Differential EquationsBackward Differentiation FormulasFinite Difference ApproximationFinite Difference DiscretizationFinite Difference SchemesNonlinear Differential-algebraic EquationsNonlinear SystemsNumerical DifferentiationNumerical Methods For Initial Value Problems
Finite difference approximations of dynamical systems modelled by nonlinear, semiexplicit, differential/algebraic equations are analyzed. Convergence for the backward differentiation method is proved for index two and index three problems when the numerical initial values obey certain constraints. The appropriate asymptotic convergence rates and the leading error terms are determined.
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