APPLICATION OF TWO STEP CONTINUOUS HYBRID BUTCHER’S METHOD IN BLOCK FORM FOR THE SOLUTION OF FIRST ORDER INITIAL VALUE PROBLEM

Abstract

The two steps Hybrid Butcher’s Method was reformulated for applications in the continuous form. The process produces some schemes which were combined in order to form an accurate and efficient block method for solution of ordinary differential equations (Ode’s). The suggested approach eliminates requirements for a starting value and its speed proved to be up when computations with the Block Discrete schemes were used. The order of accuracy and stability of the block method is discussed and its accuracy established numerically.