A family of Continuous Third Derivative Block Methods for solving stiff systems of first order ordinary differential equations

This paper presents a family of Continuous Third Derivative Block Methods (CTDBM) of order $k+3$ for the solution of stiff systems of ordinary differential equations. The approach uses the collocation and interpolation technique to generate the main Continuous Third Derivative method (CTDM) which is then used to obtain the additional methods that are combined as a single block methods. Analysis of the methods show that the method is L-stable up to order eight. Numerical examples are given to illustrate the accuracy and efficiency of the proposed method.