Second Derivative Backward Differentiation Type Block Formulae for Ordinary Differential Equations – K. O.Muka and F. O. Otunta
The second derivative parallel block backward differentiation type formulas suffer zero instability for block size greater than six. This paper seeks to restructure the second derivative parallel block backward differentiation type formulas so as to develop a family of methods that overcomes zero instability. Condition upon which the new methods are zero-stable apiori is derived. The new method developed in this paper are also A-stable for block sizes up to four.