论文信息 - A new type of shooting method for nonlinear boundary value problems

A new type of shooting method for nonlinear boundary value problems

Abstract In this article we introduce a new type of iterative method for initial value problems (IVPs). We enhance this method by using shooting techniques and interpolation for the boundary value problems. Our method is more accurate and applicable than built in methods used in different software packages. We solved several examples for initial value problems and linear and non-linear boundary value problems and compared results to those obtained using MATLAB.

Sarah Farrukh | M. Ahsan | Muhammad Ahsan | S. Farrukh

[1] Ronald B. Guenther,et al. An Introduction to Numerical Methods , 2018 .

[2] Tasawar Hayat,et al. The application of homotopy analysis method to thin film flows of a third order fluid , 2008 .

[3] Chein-Shan Liu,et al. Efficient Shooting Methods for the Second-Order Ordinary Differential Equations , 2006 .

[4] H. Keller. Numerical Solution of Two Point Boundary Value Problems , 1976 .

[5] R. Mattheij,et al. An Efficient Algorithm for Solving General Linear Two-Point BVP , 1984 .

[6] H. Bock,et al. A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems , 1984 .

[7] H. Schlichting. Boundary Layer Theory , 1955 .

[8] David D. Morrison,et al. Multiple shooting method for two-point boundary value problems , 1962, CACM.

[9] Chein-Shan Liu,et al. The Lie-Group Shooting Method for Nonlinear Two-Point Boundary Value Problems Exhibiting Multiple Solutions , 2006 .

[10] Chein-Shan Liu,et al. The Lie-Group Shooting Method for Singularly Perturbed Two-Point Boundary Value Problems , 2006 .

[11] Johannes P. Schlöder,et al. Complementary Condensing for the Direct Multiple Shooting Method , 2009, HPSC.