Physical Sciences and Mathematics Commons^™

Numerical And Approximate Analytic Solutions Of Second- Order Nonlinear Boundary Value Problems, Chein-Shan Liu, Jian-Hung Shen, Yung-Wei Chen

Journal of Marine Science and Technology

The shooting method consists of guessing unknown initial values, transforming a second-order nonlinear boundary value problem (BVP) to an initial value problem and integrating it to obtain the values at the right end to match the specified boundary condition, which acts as a target equation. In the shooting method, the key issue is accurately solving the target equation to obtain highly precise initial values. Due to the implicit and nonlinear property, we develop a generalized derivative-free Newton method (GDFNM) to solve the target equation, which offers very accurate initial values. Numerical examples are examined to show that the shooting method …