Diagonally Implicit Super Class of Block Backward Differentiation Formula with Off�?¢�?�?��?Step Points for Solving Stiff Initial Value Problems

[摘要] A new formula called 2-point diagonally implicit super class of BBDF with two off-step points (2ODISBBDF) for solving stiff IVPs is formulated. The method approximates two solutions with two off-step points simultaneously at each iteration. By varying a parameter ρ ∈ (–1,1) in the formula, different sets of formulae can be generated. A specific choice of ρ =3/4  is made and it was shown that the method is both zero and A-stable. A comparison between the new method and the existing 2-point block backward differentiation formula with off-step points (2OBBDF) is made. The results show that the new method outperformed existing 2OBBDF method in terms of accuracy.

[关键词] Off-step;Diagonally implicit super class of block backward differentiation formula;Stiff IVPs;Implicit lock method;A-stability