Diagonally implicit extended 2-point super class of block backward differentiation formula with two off-step points for solving first order stiff initial value problems

Abstract

A new diagonally implicit extended 2-point super class of block backward differentiation formula with two off– step points is developed for the solution of first order stiff initial value problems. The method computes two solution values with two off–step points concurrently at each integration step. The method is of order five. Sets of different formulae can be generated from the method by varying a free parameter   −( ) 1,1 in the formula. A specific choice of the value of the parameter  within the interval is made and the method is found to be consistent, zero stable and convergent. The region of absolute stability is plotted and it indicated that the method is A-stable. The numerical results obtained demonstrated efficiency of the new method when compared with some existing implicit numerical block methods. The developed method performed better than some existing algorithms in terms of accuracy and competes with others in terms of execution time