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 solvednumerically using shooting method which involved shooting based on secant methodand shooting based on Newton Raphson’s method. The boundary value problemswere first reduced to the solution of initial value problem where the solutions wereobtained with the aid of MATLAB. Shooting method with secant and shooting withNewton’s then applied when our approximate solution did not converge within theprovided error tolerance. After that, the numerical results obtained then beingcompared with the exact solution and Finite Difference Method to check theefficiency and accuracy of using shooting method in solving the non-linear two-pointboundary value problems. The results for Finite Difference method were obtained byMaple 2015. It was observed that shooting method with secant method and shootingmethod with Newton Raphson’s method were efficient in solving the non-linearboundary value problems, however both type of shooting need more iteration inorder to get the same accuracy as Finite Difference Method in obtaining approximatesolutions close to exact solutions.