A Non-Linear Shooting Method For Two-Point Boundary Value Problems

Abstract

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.