Linear array of permutations is hard to be factorised. However, by using a starter set, the process of listing the permutations becomes easy. Once the starter sets are obtained, the circular and reverse of circular operations are easily employed to produce distinct permutations from each starter set. However, a problem arises when the equivalence starter sets generate similar permutations and, therefore, willneed to be discarded. In this paper, a new recursive strategy is proposed to generate starter sets that will not incur equivalence by circular operation. Computational advantages are presented that compare the results obtained by the new algorithm with those obtained using two other existing methods. The result indicates that the new algorithm is faster than the other two in time execution.
This paper describes the development of a two-point implicit code in the form of fifth order Block Backward Differentiation Formulas (BBDF(5)) for solving first order stiff Ordinary Differential Equations (ODEs). This method computes the approximate solutions at two points simultaneously within an equidistant block. Numerical results are presented to compare the efficiency of the developed BBDF(5) to the classical one-point Backward Differentiation Formulas (BDF). The results indicated that the BBDF(5) outperformed the BDF in terms of total number of steps, accuracy and computational time.