Modified Adomian Decomposition Method for Double Singular Boundary Value Problems

where f(t),g(t), and h(t) are known continuous functions of t in the interval (0,1). Here N(u) is a nonlinear function of u. Let the above equation be singular at these two boundary value points t= 0,1. Scientists and engineers are interested in singular BVPs because they arise in a wide range of applications, such as in chemical engineering, mechanical engineering, nuclear industry, and nonlinear dynamical systems and solitons [1]-[8]. Therefore, this kind of problem has been studied by many researchers. For example, the existence of the solution of this type of equation has been widely studied in [9]-[10]. Numerical methods such as Adomian decomposition method (ADM) [11], fast FourierGalerkin methods [12], finite difference method [13], Chebyshev economizition [14], differential transform method [15], and iterative shooting method [16] were investigated during the past years. Generally, it is not easy to produce a good approximation for classical numerical methods. For example, you can not use the ADM directly to study the double singular BVP because the two boundary values are just singular.