Shooting method with root finding algorithm to solve boundary value problems

Abstract

One important numerical method for converting Boundary Value Problems (BVPs) into Initial Value Problems (IVPs) is the shooting method, which is mostly used as a root-finding technique. Until the boundary conditions are met, this approach entails making initial-condition predictions and iteratively improving them. Since it guarantees that the initial values yield a solution that satisfies the given boundary conditions, root discovery plays a critical role. Although the shooting approach works well, it can be sensitive to initial estimates, which can sometimes cause convergence problems. Therefore, choosing the right root-finding techniques becomes essential. Thus, this study will assess how well the shooting method performs when paired with various root-finding algorithms to solve BVPs. The effectiveness of these algorithms is compared based on their convergence rate, accuracy, and robustness. The results demonstrate the effectiveness of combining the shooting method with root-finding algorithms to deliver accurate and efficient solutions to BVPs, making it a valuable tool in scientific and engineering applications.