# Equilibrium attractive properties of a class of multistep Runge-Kutta methods

@article{Xiao2006EquilibriumAP, title={Equilibrium attractive properties of a class of multistep Runge-Kutta methods}, author={Ai-guo Xiao and Yifa Tang}, journal={Appl. Math. Comput.}, year={2006}, volume={173}, pages={1068-1081} }

## 2 Citations

### Strongly Regular General Linear Methods

- MathematicsJ. Sci. Comput.
- 2020

This paper considers the conditions that guarantee regularity and strong regularity properties of a general linear method to derive a family of variable order strongly regular general linear methods of order as high as six.

### Ultraviolet photosensitivity of sulfur-doped micro- and nano-crystalline diamond

- Materials Science, Chemistry
- 2011

The room-temperature photosensitivity of sulfur-doped micro-, submicro-, and nano-crystalline diamond films synthesized by hot-filament chemical vapor deposition was studied. The structure and…

## References

SHOWING 1-10 OF 18 REFERENCES

### High order algebraically stable multistep Runge-Kutta methods

- Mathematics, Computer Science
- 1987

Some of the stability properties of a special class of multivalue methods called multistep Runge-Kutta methods are examined and families of algebraically stable methods of arbitrarily high order are constructed.

### A stability property of implicit Runge-Kutta methods

- Mathematics, Computer Science
- 1975

A class of implicit Runge-Kutta methods is shown to possess a stability property which is a natural extension of the notion ofA-stability for non-linear systems.

### Non-linear stability of a general class of differential equation methods

- Mathematics, Computer Science
- 1980

For a class of methods sufficiently general as to include linear multistep and Runge-Kutta methods as special cases, a concept known as algebraic stability is defined, based on a non-linear test problem, which enables estimates of error growth to be provided.

### Stability Criteria for Implicit Runge–Kutta Methods

- Mathematics, Economics
- 1979

A comparison is made of two stability criteria. The first is a modification to nonautonomous problems of A-stability and the second is a similar modification of B-stability. It is shown that under…

### A special stability problem for linear multistep methods

- Mathematics
- 1963

The trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. For this method error bounds are derived which are valid under rather…

### Equilibrium attractivity of Krylov-W-methods for nonlinear stiff ODEs

- Computer Science
- 1998

This work discusses different additional assumptions onf and conditions on the Arnoldi process that imply this kind of attractivity to equilibrium points for the numerical solution of quasilinear parabolic systems.

### Equilibria of Runge-Kutta methods

- Mathematics
- 1990

SummaryIt is known that certain Runge-Kutta methods share the property that, in a constant-step implementation, if a solution trajectory converges to a bounded limit then it must be a fixed point of…

### B -convergence properties of multistep Runge-Kutta methods

- Computer Science, Mathematics
- 1994

It is proved that the family of algebraically stable r-step s-stage multistep Runge-Kutta methods with parameters al, a2, . . . , ar is optimally Bconvergent of order at least s, and B-converting of order s + 1 if some other additional conditions are satisfied.

### B -Theory of Runge-Kutta methods for stiff Volterra functional differential equations

- Mathematics
- 2003

B -stability and B -convergence theories of Runge-Kutta methods for nonlinear stiff Volterra functional differential equations (VFDEs) are established which provide unified theoretical foundation for…