Order and convergence analysis of the new fixed coefficient diagonally implicit block backward differentiation formula for the numerical solution of stiff ordinary differential equations

Abstract

This research explores the utilization of the existing new fixed coefficient diagonally implicit block backward differentiation formula for solving stiff initial value problems. The study includes the derivation of the method’s order of accuracy and its associated error constant. Convergence analysis confirms that the method satisfies the sufficient and necessary conditions of consistency and zero-stability respectively. The effectiveness of the method is validated through comparative analysis involving both numerical and theoritical solutions for selected stiff problems. Results reveal that the method maintains stability and achieves enhanced accuracy as the step size diminishes, demonstrating its suitability for stiff ordinary differential equations.