A Non-Linear Shooting Method For Two-Point Boundary Value Problems - Jumri, Nurrin Jazlina; Md Shab, Noorzehan Fazahiyah (Enhanced Knowledge in Sciences and Technology, 2021)
In this research, non-linear two-point boundary value problems were solved numerically using shooting method which involved shooting based on secant method and shooting based on Newton Raphson’s method. The boundary value problems were first reduced to the solution of initial value problem where the solutions were obtained with the aid of MATLAB. Shooting method with secant and shooting with Newton’s then applied when our approximate solution did not converge within the provided error tolerance. After that, the numerical results obtained then being compared with the exact solution and Finite Difference Method to check the efficiency and accuracy of using shooting method in solving the non-linear two-point boundary value problems. The results for Finite Difference method were obtained by Maple 2015. It was observed that shooting method with secant method and shooting method with Newton Raphson’s method were efficient in solving the non-linear boundary value problems, however both type of shooting need more iteration in order to get the same accuracy as Finite Difference Method in obtaining approximate solutions close to exact solutions.