A hybrid collocation method for solving highly nonlinear boundary value problems

In this article, a hybrid collocation method for solving highly nonlinear boundary value problems is presented. This hybrid method combines Chebyshev collocation method with Laplace and differential transform methods to obtain approximate solutions of some highly nonlinear two-point boundary value problems of ordinary differential equations. The efficiency of the method is demonstrated by applying it to ordinary differential equations modelling Darcy-Brinkman-Forchheimer momentum problem, laminar viscous flow problem in a semi-porous channel subject to transverse magnetic field, fin problem with a temperature-dependent thermal conductivity, transformed equations modelling two-dimensional viscous flow problem in a rectangular domain bounded by two moving porous walls and two-dimensional constant speed squeezing flow of a viscous fluid between two approaching parallel plates. The results obtained are compared with the existing methods and the results show that the new method is quite reasonable, accurate and efficient. Mathematics; Applied mathematics; Computational mathematics; Computational fluid dynamics; Applied computing; Laplace and differential transform methods; Nonlinear boundary value problems; Hybrid collocation; Chebyshev polynomials