Application of smart collocation method for solving strongly nonlinear boundary value ordinary differential equations

In this study, a new simple technique called, “smart collocation” is presented. This method is an extension of the collocation method for solving strongly nonlinear boundary value ordinary differential equations. Effects of varying the iteration steps, degree of nonlinearity and position of the collocation points in each sub-interval are investigated. To verify, the calculated results are compared with the bvp4c MATLAB function results. It is shown that, in the case of strongly nonlinear equations, more accurate results can be achieved by moving the position of the collocation points in sub-intervals. For a general problem, based on the degree of nonlinearity, a criterion for selecting appropriate collocation points is obtained. It is shown that varying the position of collocation points or simply smart collocation method can obviously increase accuracy of the solution.