Three new approaches for solving a class of strongly nonlinear two-point boundary value problems

Abstract Three new and applicable approaches based on quasi-linearization technique, wavelet-homotopy analysis method, spectral methods, converting two-point boundary value problem to Fredholm–Urysohn integral equation are proposed for solving a special case of strongly nonlinear problems, namely Troesch problem. A technique is utilized reduce the sequence linear equations in first method. Second method devoted applying generalized Coiflet scaling functions homotopy approximating numerical solution equation. In third we use an interesting convert Urysohn–Fredholm second kind; afterwards Simpson quadrature employed obtained Introduced methods computationally attractive, applications demonstrated through illustrative examples. Comparing results presented with some other existing this kind implies high accuracy efficiency suggested schemes.