Variational iteration method for autonomous ordinary differential systems
Applied Mathematics and Computation
Homotopy perturbation method: a new nonlinear analytical technique
Applied Mathematics and Computation
Variational iteration method for solving Burger's and coupled Burger's equations
Journal of Computational and Applied Mathematics
Variational iteration method: New development and applications
Computers & Mathematics with Applications
Simulation of micropolar fluid flow in a vertical channel using homotopy-perturbation method
ACC'08 Proceedings of the WSEAS International Conference on Applied Computing Conference
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Study of convergence of homotopy perturbation method for systems of partial differential equations
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Solution of delay differential equations via a homotopy perturbation method
Mathematical and Computer Modelling: An International Journal
A study on the convergence of variational iteration method
Mathematical and Computer Modelling: An International Journal
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Perturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear problems. To overcome this shortcoming, two new but powerful analytical methods are introduced to solve nonlinear heat transfer problems in this article; one is He's variational iteration method (VIM) and the other is the homotopy-perturbation method (HPM). The VIM is to construct correction functionals using general Lagrange multipliers identified optimally via the variational theory, and the initial approximations can be freely chosen with unknown constants. The HPM deforms a difficult problem into a simple problem which can be easily solved. Nonlinear convective-radiative cooling equation, nonlinear heat equation (porous media equation) and nonlinear heat equation with cubic nonlinearity are used as examples to illustrate the simple solution procedures. Comparison of the applied methods with exact solutions reveals that both methods are tremendously effective.