IMA Journal of Numerical Analysis · 1990 · 52 citations · 0 references
Natural SciencesMathematicsComputational MechanicsDifferential EquationsDynamical SystemsIntegral EquationsNumerical AnalysisNumerical ConvergenceNumerical Methods For Differential EquationsNumerical StabilityStability TheoryNumerical Methods For Integral EquationsNumerical Stability AnalysisStability Of Numerical SchemesVolterra EquationsVolterra Integral Equations
Stability analysis of Volterra-Runge-Kutta methods based on the basic test equation of the form where λ is a complex parameter, and on the convolution test equation where λ and σ are real parameters, is presented. General stability conditions are derived and applied to construct numerical methods with good stability properties. In particular, a family of second-order Vo-stable Volterra-Runge-Kutta methods is obtained. No Vo-stable methods of order greater than one have been presented previously in the literature.