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Mathematics of Computation

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

Author: Shou Fu Li
Journal: Math. Comp. 62 (1994), 565-575
MSC: Primary 65L06
MathSciNet review: 1201071
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Abstract: By using the theory of B-convergence for general linear methods to the special case of multistep Runge-Kutta methods, a series of B-convergence results for multistep Runge-Kutta methods is obtained, and it is proved that the family of algebraically stable r-step s-stage multistep Runge-Kutta methods with parameters $ {\alpha _1},{\alpha _2}, \ldots ,{\alpha _r}$ presented by Burrage in 1987 is optimally Bconvergent of order at least s, and B-convergent of order $ s + 1$, provided that $ r \geq s$ and $ {\alpha _j} > 0,j = 1,2, \ldots ,r$. Furthermore, this family of methods is optimally B-convergent of order $ s + 1$ if some other additional conditions are satisfied.

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Article copyright: © Copyright 1994 American Mathematical Society