## On the Construction of Highly Stable, Explicit, Numerical Methods for Integrating Coupled Ordinary Differential Equations with Parasitic Eigenvalues |

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_ n+i accuracy ah|c associated matrix calculations characteristic equation coefficients computation conditionally stable constructed COUPLED ORDINARY DIFFERENTIAL crh|c derived difference equations differenced discussed driving eigenvalues e-iooox effect of roundoff elements equation 28a equation 33 Equation 46a equations 27 EQUATIONS WITH PARASITIC Error in uncoupled exact solution explicit methods final corrector fourth-order Runge-Kutta method given by equation given step imaginary implicit induced stability boundary inherently stable iterations kth ORDER l.OOOOOOOOOE+OO l6 place LAnJ large negative eigenvalues largest parasitic eigenvalue magnitude matrix given maximum methods represented modified Euler method Moffett Field nonautonomous nonlinear equations numerical integration One-Root Methods ordinary differential equations parasitic eigen predictor-corrector sequence given real eigenvalues real induced stability real stability polynomial reference representative equation root roundoff error shown in sketch significant figures sketch h SQUARES STABILITY POLYNOMIAL Taylor series term tion truncation error un+1 un+i values of ah vector wn+i zero