A new approach to solve a set of nonlinear split boundary value problems

In this paper, we propose a new approach based on conjunction of the orthogonal collocation on finite elements method with decoupling and quasi-linearization technique to approximate solutions of a set of nonlinear split boundary value problems. The numerical stability, the convergence and the accuracy of the results are checked by this algorithm. The approach developed in this study is illustrated by some numerical examples. These examples are solved using a special software package which implements the proposed algorithms.

► New approach to solve nonlinear split boundary value problems was developed.
► In this method, the problem is reduced to linear algebraic equations.
► A small number of collocations points give a satisfactory precision.
► This method solves the gas separation systems for mixture more than three components.