Finite-Difference Methods for Linear Problems➢The linear and nonlinear Shooting methods for boundary-value problems can present problems of instability.➢The methods in this section have better stabilitycharacteristics.➢However, they generally require more computation to obtain aspecified accuracy.➢Methods involving finite differences for solving boundary-value problems replace each of the derivatives in thedifferential equation with an appropriate difference-quotientapproximationof the type considered in Section 4.1.➢The particular difference quotient and???? ?𝑖?? ℎare chosento maintain a specified order oftruncation error.➢However,ℎcannot be chosen too small because of thegeneral instability of the derivative approximations.Discrete ApproximationThe finite difference method for the linear second-orderboundary-value problem,