A UNIFORM ORDER CONTINUOUS HYBRID INTEGRATION FOR SOLVING THIRD ORDER ORDINARY DIFFRENTIAL EQUATIONS

Abstract

A three -step Continuous Block Hybrid Method (CBHM) with two non-step points of order (6,6,6,6,6) is proposed for direct solution of the special and general third order initial value problems (IVPs). The main method and additional methods are obtained from the same continuous schemes derived via interpolation and collocation procedures. The stability properties of the methods are discussed and the stability region shown. The methods are applied in block form as simultaneous numerical integrators over non-overlaping interval. The efficiency of the proposed method was tested and was found to compete favorable with the existing methods.