A NEW 2-POINT DIAGONALLY IMPLICIT VARIABLE STEP SIZE SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING FIRST ORDER STIFF INITIAL VALUE PROBLEMS - Najamuddeen, Bala; Hamisu, Musa; Abba, Sani (FUDMA JOURNAL OF SCIENCES, 2025)
A new 2-point diagonally implicit variable step size super class of block backward differentiation formula (2DVSSBBDF) for solving first order stiff initial value problems (IVPs) is developed. The method is derived by introducing a lower triangular matrix in the coefficient matrix of existing 2-point variable step size superclass of block backward differentiation formula for the integration of stiff IVPs. The order of the method is 4. The stability analysis indicates that the method is both zero and A-stable.  The Numerical results obtained are compared with some existing built in Matlab ODEs solvers in particular ODE15s and ODE23s and the performance of the new scheme showed an advantage in accuracy and computation time over some existing algorithms. The new method can serve as an alternative and efficient method for solving stiff IVPs.
Keywords: Diagonally implicit block method; Variable step size; Stiff, Order; Zero stability; Blocks backward differentiation formula; A–Stability