论文信息 - The Convergence of Variable-Stepsize, Variable-Formula, Multistep Methods

The Convergence of Variable-Stepsize, Variable-Formula, Multistep Methods

In this paper variable-stepsize, variable-formula, multistep methods for the numerical solution of ordinary differential equations are considered. Some more general results on stability than are given in the papers of Gear–Tu [SIAM J. Numer. Anal., 11 (1974), pp. 1025–1043] and Gear–Watanabe [SIAM J. Numer. Anal., 11 (1974), pp. 1044–1058] are obtained. Further, the asymptotic behavior of the error in the variable-stepsize, fixed-formula case is studied. Finally, the above study is extended to predictor-corrector methods.

M. Crouzeix | F. Lisbona | M. Crouzeix | F. J. Lisbona

[1] C. W. Gear,et al. The automatic integration of stiff ordinary differential equations , 1968, IFIP Congress.

[2] Kenneth Ronald Jackson. Variable stepsize, variable order integrand approximation methods for the numerical solution of ordinary differential equations. , 1978 .

[3] Peter Piotrowski. Stability, consistency and convergence of variable K-step methods for numerical integration of large systems of ordinary differential equations , 1969 .

[4] Ron Sacks-Davis,et al. An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs , 1980, TOMS.

[5] Zahari Zlatev,et al. Stability properties of variable stepsize variable formula methods , 1978 .

[6] C. W. Geart,et al. THE EFFECT OF VARIABLE MESH SIZE ON THE STABILITY OF MULTISTEP METHODS , 1974 .

[7] R. Brayton,et al. A new efficient algorithm for solving differential-algebraic systems using implicit backward differentiation formulas , 1972 .

[8] Charles William Gear,et al. Stability and convergence of variable order multistep methods , 1974 .

[9] Charles William Gear,et al. The Stability of Automatic Programs for Numerical Problems , 1974 .

[10] G. Dahlquist. Convergence and stability in the numerical integration of ordinary differential equations , 1956 .

[11] C. W. Gear,et al. Initial value problems: practical theoretical developments , 1979 .