A proposed rational numerical one-step integrator of order eight for initial value problems

K. Ponnammal; V. Prabu

doi:10.26637/MJM0703/0027

Abstract

In this paper, we derive a one-step rational numerical integrator of order eight for solving stiff and non-stiff initial value problems (IVP). It is proved that the proposed method is consistent and convergent. It is also found that the method is L-stable. Numerical result shows that the proposed method is efficient and accurate.

Keywords:

Rational numerical integrator, Convergent, Stability

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

K. Ponnammal PG and Research Department of Mathematics, Periyar E. V. R. College, Tiruchirappalli-620023, Tamil Nadu, India.
V. Prabu PG Assistant in Mathematics, Government Higher Secondary School, Nerkunam-604406, Tamil Nadu, India.

Pages: 532-540
Date Published: 01-07-2019
Vol. 7 No. 03 (2019): Malaya Journal of Matematik (MJM)

R.L.Burden, J.D. Faires, Numerical Analysis, 5-th Edition, Boston, PWS Publishing Company, (1993).

J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations, $2^{text {nd }}$ revised edition, England John Wiley & Sons, (2008).

S.O. Fatunla, Numerical Treatment of Singular / Discontinuous IVPs, Journal Computers Math. Appl., $12 mathrm{~b}(5 / 6)(1986), 109-115$.

S.O. Fatunla, Numerical Methods for IVPs in ODES, Academic Press, Boston, USA, (1988).

S.O. Fatunla, On the numerical solution of Singular IVPs, ABACUS, 19(2)(1990), 121-130.

S.O. Fatunla, Recent Development in the Numerical Treatment of Singular; Discontinuous IVPS, Scientific Computing (ed. S.O. Fatunla), Ada + Jane Press, (1994), $46-60$.

S.O. Fatunla and U.S.L.J. Aashikpelokhai, A Fifth order L-stable Numerical integrate, Scientific Computing (S.O. Fatunla Ed), (1994), 68-86.

M.N.O. Ikhile, Coefficients for studying one-step rational schemes for IVPs in ODEs:I, Computers and Mathematics with Applications, 41(2001), 769-781.

J.D. Lambert and B. Shaw, On the numerical solution of $y^{prime}=f(x, y)$ by a class of formulae based on rational approximation, Math. Comp., 19(1965), 456-462.

J.D. Lambert, Nonlinear methods for stiff system of ODES, Conference on the Numerical Solutions of ODEs, Dundee, (1974), 77-88.

Y.L. Luke, Fair, W. and Wimp, J. Predictor - Corrector formulas based on Rational Interpolants, Journal Computer and Maths with Applications, 1(1975), 302-307.

F.O. Otunta and M.N.O. Ikhile, Stability and Convergence of a Class of Variable order non-linear one-step Rational Integrators of IVPs in ODEs, International Journal of Computer Mathematics, 62(1996), 199-208.

F.O. Otunta and M.N.O. Ikhile, Efficient Rational onestep Numerical Integrators for Initial Value Problems in Ordinary Differential Equations, International Journal of Computer Mathematics, 72(1999), 49-61.

F.O. Otunta and G.G. Nwachukwu, An R [2, 3; 1:5] Rational one-step Integrators for Initial Value Problems in Ordinary Differential Equations, Nigerian Journal of Mathematics and Applications, 16(2)(2003), 146-158.

F.O. Otunta and G.C. Nwachukwu, Rational one-step Numerical Integrator for Initial Value Problems in Ordinary Differential Equations, Journal of the Nigerian Association of Mathematical Physics, 9(2005), 285-294.