The equivalence of algebraic stability andAN-stability
Copyright policy )The equivalence of algebraic stability andAN-stability
Let C be a general linear integration method. The author proves that an irreducible AN-stable method C is algebraically stable (for definitions of these concepts see the author [ibid. 27, 182-189 (1987; Zbl 0623.65074)]. This generalizes previous results about Runge-Kutta methods and one-leg methods. A number of useful miscellaneous results from theory of matrices are presented in the paper as well.
- University of Auckland New Zealand
irreducible AN-stable method, Runge-Kutta methods, one-leg methods, linear integration method, algebraic stability, Nonlinear ordinary differential equations and systems, Stability and convergence of numerical methods for ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations
irreducible AN-stable method, Runge-Kutta methods, one-leg methods, linear integration method, algebraic stability, Nonlinear ordinary differential equations and systems, Stability and convergence of numerical methods for ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations
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