STABILITY ANALYSIS OF A PROPOSED SCHEME OF ORDER FIVE FOR FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
Sunday Emmanuel Fadugba1*, Roseline Bosede Ogunrinde2 and Rowland Rotimi Ogunrinde3
1,2 Department of Mathematics, Ekiti State University, Ado Ekiti, Nigeria
3 Department of Mathematical Sciences, Augustine University, Ilara Epe, Lagos State, Nigeria
This paper presents the stability analysis of a proposed scheme of order five (FCM) for first order Ordinary Differential Equations (ODEs). The proposed FCM is derived by means of an interpolating function of polynomial and exponential forms. The properties of FCM were discussed extensively. The linear stability of FCM in the context of the Third Order One-Step Method (TCM) and Second Order One-Step Method (SCM) for the solution of initial value problems of first order differential equations is presented. The stability region of FCM, TCM and SCM is investigated using the Dahlquist’s test equation. The numerical results obtained via FCM are compared with TCM and SCM. Moreover, by varying the step length, the accuracy and convergence of the methods in terms of the final absolute relative error are measured. The results show that FCM converges faster and more stable than its counterparts.
Keywords: Fifth order scheme, final absolute relative error, initial value problem, second order method, stability, third order method.
Published On: 21 September 2021