Applications of HAM and OHAM to Solve System of Reaction Problems

This paper describes a technique of homotopy analysis method (HAM) that designed to show the powerful of this technique in approximating solutions the system of differential equations reaction problems in chemistry. Three systems of ODEs given to solve by three approaches by choosing different value of.  Optimal Homotopy Asymptotic Method (OHAM) considered to find optimal control parameter 3 2, 1, = i , i  and minimize residual error. We considered comparison of logplot error for examples. Residual and absolute errors are presented to show the effect of HAM. A convergence theorem for the series solution of ODEs system is also given. Moreover, the tables and figures show the method analytical and approximating the solutions very well.

nonlinear system of differential equations, homotopy analysis method, reaction problems, residual error, Optimal Homotopy Asymptotic Method, Convergence