Application of the shooting method in 2-point block BDF for nonlinear boundary value problems - Soomro, Hira; Nooraini, Zainuddin; Nor Ain Azeany, Mohd Nasir; Hanita, Daud; Rahimah, Jusoh; Siti Ainor, Mohd Yatim; Iskandar Shah, Mohd Zawawi (International Association of Engineers, 2025)
In this research, the boundary value problems (BVPs) are solved by applying a variable step two-point block backward differentiation formula (2BDF) in a shooting technique. An iterative procedure known as Newton-Raphson and the linear combination of the initial guesses are applied in this shooting approach to find appropriate initial conditions for a related initial value problem (IVP) of BVP. Initially, the nonlinear BVP is reduced to the form of first-order ordinary differential equation (ODE). Subsequently, the missing IVP is approximated using the shooting technique and then solved by the 2BDF. Comparisons to exact solutions demonstrate the outcome of the proposed method for solving nonlinear BVP. The results show that the application of shooting technique is appropriate for the 2BDF to solve nonlinear BVP.