STABILITY OF ONE-STEP SCHEME INTERPOLATION FUNCTION IN ORDINARY DIFFERENTIAL EQUATIONS.

Ebhohimen F. , Anetor O. and Osemwegie U.I.

Department of Mathematics,Faculty of physical sciences, Ambrose Alli University P.M.B.14, Ekpoma. Edo tate, Nigeria.

Department of Mathematics’ College of Education, Ekiadolo-Benin, Edo State,Nigeria.

Abstract

In this research work, we consider the stability of one-step scheme interpolation function in ordinary differential equations of the form: 

F(x)=ao + a1x + btan (ρx + σ),where ao, a1 and b are real undetermined coefficient, ρ and σ are complex parameters. We consider the linear multistep method in the 

 where  and  are constants and .The Taylor’s series expansion of y(xt+1) about x = xt is     was also implemented to establish our result at k=5.

Keyhword: Interpolation Function, Stability, Consistency and Convergence