Abstract
An implicit Runge-Kutta method, applied to an initial value problem, gives systems of algebraic equations. Under natural assumptions concerning the differential system, there are known conditions on the method which guarantee that the algebraic equations have unique solutions. It is shown that these conditions are closely related to the requirement that the method be (k(l),l)-algebraically stable on an interval [0,α).
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Cooper, G.J. Algebraic stability and the existence of solutions of implicit Runge-Kutta equations. BIT 25, 386–390 (1985). https://doi.org/10.1007/BF01934382
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DOI: https://doi.org/10.1007/BF01934382