Fixed Coefficient A ( α ) Stable Block Backward Differentiation Formulas for Stiff Ordinary Differential Equations

Abstract

The main contribution in this paper is to construct an implicit fixed coefficient Block Backward Differentiation Formulas denoted as A ( α ) -BBDF with equal intervals for solving stiff ordinary differential equations (ODEs). To avoid calculating the differentiation coefficients at each step of the integration, the coefficients of the formulas will be stored, with the intention of optimizing the performance in terms of precision and computational time. The plots of their A ( α ) stability region are provided, and the order of the method is also verified. The necessary conditions for convergence, such as the consistency and zero stability of the method, are also discussed. The numerical results clearly showed the efficiency of the method in terms of accuracy and execution time as compared to other existing methods in the scientific literature.