Singly diagonally implicit block BDF of order 3 for stiff ordinary differential equations

This paper presents the development of a Singly Diagonally Implicit Block Backward Differentiation Formula (SDIBBDF) of order 3 for solving stiff Ordinary Differential Equations (ODEs). The general formula is derived using Taylor series expansion, yielding two approximate solutions that are computed simultaneously in a block. The proposed method is shown to be zero-stable, consistent, convergent and A-stable. Numerical results based on maximum error and execution time, indicate that the proposed method outperforms the existing methods in solving stiff ODEs.