ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 65L05, 65L10, 65D30 Chawla, M. M., Al-Zanaidi, M. A., Evans, , D. J. 1,2 Department of Mathematics and Computer Science, Kuwait University, P. O. Box 5969, Safat, 13060 Kuwait, 3 Department of Computer Studies, Loughborough University of Technolog, Loughborough, Leicestershire LE11 3TU, UK A Class of Generalized Trapezoidal Formulas for the Integration of y’=f(x, y) A one-parameter family of generalized trapezoidal formula (GTFs) is introduced, which include both the A-stable classical arithmetic mean (AM) trapezoidal formula and an L-stable modified arithmetic mean (MAM) trapezoidal formula of Chawla and Al-Zanaidi [1]. The generalized trapezoidal formula (GTFs) include both the AM and MAM trapezoidal formula as special cases. A GTF can switch from an A-stable to an L-stable method depending on parameter values, and it is shown to perform, for certain selection of the parameter values, better than AM and MAM formula for the integration of examples of the stiff systems considered. Reference: [1] Chawla, M. M. and Al-Zanaidi, M. A., New L-stable modified trapezoidal formula for numerical integration of y’=f(x, y), Intern. J. computer math. ,Vol. 63 pp. 279-288.