BLOCK BACKWARD DIFFERENTIAL FORMULA FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

ABSTRACT

This paper's primary focus is on developing an implicit method with variable step size, based on the Backward Differentiation Formulae (BDF), for solving stiff initial value problems (IVPs) of first-order Ordinary Differential Equations (ODEs). This method, known as the 2-point Block Backward Differentiation Formula (BBDF), generates two solution values simultaneously. The paper also includes graphical representations of the regions of absolute stability for this method. The efficiency of the 2-point BBDF is then compared to a non-block BDF method with variable step and variable order (NBDF). The numerical results clearly demonstrate that the 2- point BBDF method outperforms the NBDF method in terms of both execution time and accuracy.