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- W2079247768 abstract "The root locus for the equation $M{ddot{bf y}} + S{bf y} = 0$ of undamped oscillatory motion, where M and S are symmetric, M is positive definite and S is nonnegative definite, lies on the imaginary axis of the complex plane. Consequently, it intersects the region of stability for all standard linear multistep methods of order greater than two, as shown by Dahlquist. This paper, however, presents third order linear multistep formulas which can be utilized for obtaining stable solutions for the undamped equation of motion. The solutions are obtained by applying the formulas to a companion problem $M{ddot{bf y}} + beta S{dot{bf y}} + S{bf y}$, where $beta $ is determined by the step size and the formulas used. Analysis of the accuracy for linear problems is given with numerical test results for both linear and nonlinear problems." @default.
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- W2079247768 date "1976-09-01" @default.
- W2079247768 modified "2023-09-25" @default.
- W2079247768 title "Stiffly Stable Methods for Undamped Second Order Equations of Motion" @default.
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- W2079247768 doi "https://doi.org/10.1137/0713047" @default.
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