SIMPSON'S 3/8-TYPE BLOCK METHOD FOR STIFF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
Abstract
In this paper, a self-starting second derivative multistep block method which uses the logic behind the Simpson's 3/8 rule for quadrature is derived using collocation and interpolation techniques to obtain the approximate solutions of sti dierential equations. The main method and two additional methods are assembled into a block matrix equation which is applied to provide the solutions of sti IVPs on non-overlapping intervals. The method is shown to be A-Stable, effective and reliable for sti systems of ordinary dierential equations. The order of the method is discussed and its accuracy is tested and established numerically.References
O. A. Akinfenwa, S. N.Jator and N. M. Yao, Implicit Two Step Continuous Hybrid Block Methods with Four O-Steps Points For Solving Stiff Ordinary Differential Equation, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering (2011) vol. 5(3) p213-216.
O. A. Akinfenwa, S. N.Jator and N. M. Yao, An eighth order Backward Dierentiation Formula with Continuous Coecients for Sti Ordinary Dierential Equations,International Journal of Mathematical and Computer Sciences Vol. 7(4) (2011), 171-176
L. C. BAKER, Tools for Scientist and Engineers. New York: McGraw-Hill 1989.
Brugnano L. and D. Trigiante, D., Solving Dierential Problems by Multistep Initial and Boundary Value Methods, Gordon and Breach Science Publishers, Amsterdam, 1998.
J. C. Butcher, A modified multistep method for the numerical integration of ordinary differential equations, J. Assoc. Comput. Mach. 12 (1965) 124-135.
J. R. Cash, On the exponential fitting of composite multiderivative linear multistep methods, SIAM J. Numer. Anal. 18 (1981) 808-821.
P. Chartier, L-Stable parallel one-block methods for ordinary differential equations, SIAM J. Numer. Anal. 31 (1994) 552-571.
C.F. Curtiss, J.O. Hirschfelder, Integration of sti equations, Proc. Natl. Acad. Sci. 38 (1952) 235-243.
Dahlquist, G. A Special Stability Problem for Linear Multistep Methods, BIT, 3, 1963, pp.27-43.
