Adaptive step size of diagonally implicit block backward differentiation formulas for solving first and second order stiff ordinary differential equations with applications - Mohd Ijam, Hazizah (2020)
In this thesis, new classes of block methods based on backward differentiation formula (BDF) for solving first and second order stiff ordinary differential equations (ODEs) are developed. These methods are implemented in diagonally implicit structure and generated the solutions of yn+1 and yn+2 simultaneously in a block. The formulas are constructed by taking a non zero arbitrary, incorporating a free parameter, ρ and hence producing ρ diagonally implicit block backward differ- entiation formula (ρ DIBBDF) which contain the block backward differentiation formula (BBDF) as a subclass.