A new and applicable approach based on cubic B-spline wavelets and spectral methods is applied for solving a special case of strongly nonlinear two-point boundary value problems, namely Troesch problem. The purposed method is devoted to application of cubic B-spline wavelets and their operational matrix of derivative via Galerkin and collocation methods to approximate the numerical solution of Troesch equation. Comparison the results of presented method with the results of some other exiting methods for solving this kind of equations, show the high accuracy and efficiency of suggested scheme.
