A class of RK methods consistent of order at least 2 is offered so that the unity of thetwo-stage Gauss, Radau and Lobatte formulae is achieved. Based on the class of axmethods exponentially fitted ax formulae of orde...A class of RK methods consistent of order at least 2 is offered so that the unity of thetwo-stage Gauss, Radau and Lobatte formulae is achieved. Based on the class of axmethods exponentially fitted ax formulae of order 2 with two parameters and of order3 with one parameter are given, which are not only A-stable but also algebraicallystable, and therefore suitable for integration with a large stepsize for fast decayingcomponents of linear and nonlinear stiff systems.展开更多
Some new concepts of stability are introduced for general linear methods, and algebraic conditions for stability of the methods are proposed which are suitable not only for implicit methods but also for explicit metho...Some new concepts of stability are introduced for general linear methods, and algebraic conditions for stability of the methods are proposed which are suitable not only for implicit methods but also for explicit methods. Our results characterize the interrelation between linear and nonlinear stability so that new evidence for the construction of efficient and stable methods is offered.展开更多
文摘A class of RK methods consistent of order at least 2 is offered so that the unity of thetwo-stage Gauss, Radau and Lobatte formulae is achieved. Based on the class of axmethods exponentially fitted ax formulae of order 2 with two parameters and of order3 with one parameter are given, which are not only A-stable but also algebraicallystable, and therefore suitable for integration with a large stepsize for fast decayingcomponents of linear and nonlinear stiff systems.
文摘Some new concepts of stability are introduced for general linear methods, and algebraic conditions for stability of the methods are proposed which are suitable not only for implicit methods but also for explicit methods. Our results characterize the interrelation between linear and nonlinear stability so that new evidence for the construction of efficient and stable methods is offered.
