### SIMPSON'S 3/8-TYPE BLOCK METHOD FOR STIFF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS

O. A. AKINFENWA, R. I. ABDULGANIY, S. A. OKUNUGA, V. IRECHUKWU

#### 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.

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#### 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.

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