It is the purpose of the present paper to introduce an approach based on the
homotopy analysis method to solve the nonlinear initial or boundary value problems with
strongly nonlinear terms like (sqrt root, exp, sinh, cos,…). This approach reduces time
consuming in the homotopy analysis method. Advantage of proposed idea is solving the
problems without any transformation or approximation. The Sine-Gordon equation and some
examples are used as illustrative examples to show the simplicity and effectiveness of the
proposed approach. Also we solve the first extension of Bratu problem to show the proposed
approach is capable to predict and calculate all branches of the solutions simultaneously.