A family of modified backward differentiation formula (BDF) type block methods for the solution of stiff ordinary differential equations

Abstract

A family of modified BDF type block methods for the solution stiff ordinary differential equations has been constructed in this research. Four different block methods for step number, k =2, 3, 4 and 5 have been derived using the multi-step collocation approach. The stability properties of the newly constructed methods have been investigated using written computer codes and have all shown to be convergence and A-stable. The new methods are found to be suitable for computing solutions of stiff problems. The solutions of the new block methods have been compared with the corresponding exact solutions and the associated absolute errors are presented. Performance of the new methods improved as the step number increase. The implementation approach adopted, contributed both in the accuracy and in managing computation effort.