Chein-Shan Liu¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.5, No.2, pp. 55-84, 2008, DOI:10.3970/icces.2008.005.055

Abstract The present paper provides a Lie-group shooting method for the numerical solutions of second-order nonlinear boundary value problems exhibiting multiple solutions. It aims to find all solutions as easy as possible. The boundary conditions considered are classified into four types, namely the Dirichlet, the first Robin, the second Robin and the Neumann. The two Robin type problems are transformed into a canonical one by using the technique of symmetric extension of the governing equations. The Lie-group shooting method is very effective to search unknown initial condition through a weighting factor r(0,1). Furthermore, the closed-form solutions are derived to calculate the… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 149-164, 2006, DOI:10.3970/cmes.2006.013.149

Abstract The present paper provides a Lie-group shooting method for the numerical solutions of second order nonlinear boundary value problems exhibiting multiple solutions. It aims to find all solutions as easy as possible. The boundary conditions considered are classified into four types, namely the Dirichlet, the first Robin, the second Robin and the Neumann. The two Robin type problems are transformed into a canonical one by using the technique of symmetric extension of the governing equations. The Lie-group shooting method is very effective to search unknown initial condition through a weighting factor r ∈ (0,1) Furthermore, the closed-form solutions are derived… More >