A New Analytical Approach for Solving Nonlinear Boundary Value Problems in Finite Domains

Abstract

Based on the homotopy analysis method (HAM), we propose an analytical approach for solving the following type of nonlinear boundary value problems in finite domain. In framework of HAM a convenient way to adjust and control the convergence region and rate of convergence of the obtained series solutions, by defining the so-called control parameter h , is provided. This paper aims to propose an efficient way of finding the proper values of h.Such values of parameter can be determined at the any order of approximations of HAM series solutions by solving of a nonlinear polynomial equation. Some examples of nonlinear initial value problems in finite domain are used to illustrate the validity of the proposed approach. Numerical results confirm that obtained series solutions agree very well with the exact solutions.

Based on the homotopy analysis method (HAM), we propose an analytical approach for solving the following type of nonlinear boundary value problems in finite domain. In framework of HAM a convenient way to adjust and control the convergence region and rate of convergence of the obtained series solutions, by defining the so-called control parameter h , is provided. This paper aims to propose an efficient way of finding the proper values of h.Such values of parameter can be determined at the any order of approximations of HAM series solutions by solving of a nonlinear polynomial equation. Some examples of nonlinear initial value problems in finite domain are used to illustrate the validity of the proposed approach. Numerical results confirm that obtained series solutions agree very well with the exact solutions.

Cite this paper

nullJ. Biazar and B. Ghanbari, "A New Analytical Approach for Solving Nonlinear Boundary Value Problems in Finite Domains,"*Applied Mathematics*, Vol. 2 No. 8, 2011, pp. 987-992. doi: 10.4236/am.2011.28136.

nullJ. Biazar and B. Ghanbari, "A New Analytical Approach for Solving Nonlinear Boundary Value Problems in Finite Domains,"

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