Solving Stiff Ordinary Differential Equations Using Block Backward Differentiation Formulas

Abstract

This paper discussed the Block Backward Differentiation Formula (BBDF) method for solving stiff Ordinary Differential Equations (ODEs). Generally, method for solving stiff ODEs is implicit and requires Newton iteration which is very costly in terms of execution time. Therefore, two point block method using variable step size based on Backward Differentiation Formula (BDF) is developed. The BBDF code will store all the differentiation coefficients in order to prevent tedious and repetitive computation of the differentiation coefficients at every step. The efficiency of the BBDF method is compared with the conventional BDF method. Numerical results indicate that the BBDF method outperform the BDF method in both execution time and accuracy. Keywords: Block; stiff; backward differentiation formulas