Diagonally Implicit 2-Point Block Backward Differentiation Formula With Two Off-Step Points For Solving Stiff Initial Value Problems

A diagonally implicit form of the 2-point block backward differentiation formula (BDF) with two off-step points is developed for solving stiff initial value problems. The method is derived by introducing a lower triangular matrix in the coefficient matrix of the existing 2-point block BDF method with off-step points for solving stiff ordinary differential equations. The method approximates two solutions values with two off-step points simultaneously at each iteration step and its order is 5. The stability analysis of the method indicates that the method is zero-stable. The absolute stability region of the method is plotted and it indicates that the method is A-stable. Some stiff initial value problems are solved and the results obtained show that the new method outperformed an existing method in terms of accuracy. For execution time, the new method outperformed 2BBDF and has no advantage over 2OBBDF.