Three Steps Second Derivative Adams Moulton Methods for the Solution of Stiff Differential Equations

Abstract

In this paper, the continuous forms of the Second Derivative Generalized Adams methods (SDGAMs) and its hybrid formed by adding one off-grid collocation point for step number k = 3 were derived. These continuous formulations were evaluated at some desired points to give the discrete schemes which constitute the block methods. Convergence analysis was carried out on both the block methods derived and it was observed that the block methods are both consistent and zero stable, implying that they are both convergents. The block methods were implemented on the solution of some stiff initial value problems. It was observed that the second derivative hybrid generalized Adams methods (SDHGAMs) performed better than the conventional second derivative generalized Adams methods (SDGAMs) when compared with the exact solution.