Hybrid methods for direct integration of special third Order ordinary differential equations - Jikantoro, Yusuf Dauda; Ismail, Fudziah; Senu, Norazak; Ibrahim, Zarina Bibi (Elsevier, 2018)
In this paper we present a new class of direct numerical integrators of hybrid type for special third order ordinary differential equations (ODEs),y'''=f(x,y) ; namely, hybrid methods for solving third order ODEs directly (HMTD). Using the theory of B-series, order of convergence of the HMTD methods is investigated. The main result of the paper is a theorem that generates algebraic order conditions of the methods that are analogous to those of two-step hybrid method. A three-stage explicit HMTD is constructed. Results from numerical experiment suggest the superiority of the new method over several existing methods considered in the paper.