Modern Scientific Press

ABSTRACT: This paper present a semi-analytic technique to solve the quadratic eigenvalue problem using repeated interpolation polynomial. The technique finds the eigenvalue and the corresponding nonzero eigenvector which represent the solution of the equation in a certain domain. Illustration example is presented, which confirm the theoretical predictions and a comparison between suggested technique and other methods.

ABSTRACT: 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.

ABSTRACT: In this paper the analytical solution of steady state non-linear boundary value problem in phosphoinositide dynamics is discussed. The analytical expression of the receptor desensitization and the reaction-diffusion process of the phosphoinositide can be obtained using Homotopy perturbation method (HPM) for various values of the relevant parameters. In this study, the analytical results have been compared with perturbation method and which showed that, the present approach has less computational aspect and are applicable for solving other non-linear boundary value problem.