A smart nonstandard finite difference scheme for second order nonlinear boundary value problems

A new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems. An artificial parameter is introduced in the scheme. Symbolic computation is proposed for the construction of the scheme. Local truncation error of the method is discussed. Numerical examples are illustrated. Numerical results show that the method is very effective. (C) 2011 Elsevier Inc. All rights reserved.