A class of generalized trapezoidal formulas for the numerical integration of y′ = f(x,y)

International Journal of Computer Mathematics

Volumn 62, Issue 1-2, 1996, Pages 131-142

  Chawla, M M ^a   Al Zanaidi, M A ^a   Evans, D J ^b  

^a KUWAIT UNIVERSITY   (Kuwait)

^b LOUGHBOROUGH UNIVERSITY   (United Kingdom)

Author keywords

A stability; Generalized trapezoidal formula; L stability; Ordinary differential equations, initial value problem; Stiff systems; Trapezoidal formula

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; NUMERICAL METHODS; STATISTICAL METHODS;

ARITHMETIC MEAN; GENERALIZED TRAPEZOIDAL FORMULAS; INITIAL VALUE PROBLEM; MODIFIED ARITHMETIC MEAN; STIFF SYSTEMS;

INTEGRATION;

EID: 0030385580     PISSN: 00207160     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207169608804530     Document Type: Article

References (8)

1. Chawla, M. M. and Al-Zanaidi, M. A. New L-stable modified trapezoidal formulas for thé numerical integration of y′ =f (x, y), Intern. J. Computer Math., to appear.
2. Evans, D. J. and Sanugi, B. B. (1987). A comparison of numerical ODE solvers based on arithmetic and geometric means, Intern. J. Computer Math., 23, 37-62.
3. Evans, D. J and Sanugi, B.B. (1991). A comparison of nonlinear trapezoidal formulas for solving initial value problems, Intern. J. Computer Math., 41, 65-79.
4. Lambert, J. D. Stiffness; in Computational Techniques for Ordinary Differential Equations. Gladwell, I. and Sayers D. K. (ed.), Academic Press, London, pp. 19-46.
5. Lambert, J. D. (1991). Numerical Methods for Ordinary Differential Systems, John Wiley, New York.
6. Lindberg, B. (1971). On smoothing and extrapolation for the trapezoidal rule, BIT, 11, 29-52.
7. Liniger, W. and Willoughby, R. A. (1970). Efficient integration methods for stiff systems of ordinary differential equations, SIAM J. Numer. Anal., 7, 47-66.
8. Wazwaz, A.-M. (1994). On the numerical solution of y′ =f (x, y) by a class of nonlinear trapezoidal formulas, Intern. J. Computer Math., 51, 229-238.