A diagonally implicit modified extended 2-point super class of block backward differentiation formula for solving stiff initial value problems

Abstract

This work develops a diagonally implicit modified extended 2-point super-class block backward differentiation formula (DIME2SBBDF) for stiff initial value problems (IVPs). The scheme is constructed by inserting a diagonal matrix into the coefficient matrix of the existing modified extended 2-point super-class block backward differentiation formula (ME2SBBDF). Two solution values are computed per integration step. For admissible values of the free , the method is consistent and third-order accurate. When , zero-stability and A-stability are verified. Convergence is also established theoretically. The method was implemented in C and tested on linear and nonlinear stiff IVPs. Comparisons with 1BDF, 2BBDF, and ME2SBBDF show that DIME2SBBDF generally gives better accuracy. The proposed method is therefore a viable alternative for stiff IVPs.