Abstract
We will consider variational iteration method (VIM) and Padé approximant, for finding analytical solutions of the Glauert-jet (self-similar wall jet over an impermeable, resting plane surface) problem. The solutions are compared with the exact solution. The results illustrate that VIM is an attractive method in solving the systems of nonlinear equations. It is predicted that VIM can have a found wide application in engineering problems.
Highlights
Nonlinear phenomena play a crucial role in applied mathematics and physics
The solutions are compared with the exact solution
It is predicted that VIM can have a found wide application in engineering problems
Summary
Nonlinear phenomena play a crucial role in applied mathematics and physics. We know that most of engineering problems are nonlinear, and it is difficult to solve them analytically. Various powerful mathematical methods have been proposed for obtaining exact and approximate analytic solutions. The VIM is useful to obtain exact and approximate solutions of linear and nonlinear differential equations. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. It has been used to solve effectively, and accurately a large class of nonlinear problems with approximation 4, 5 It was shown by many authors 6–16 that this method is more powerful than existing techniques such as the Adomian method 17, 18. The motivation of this letter is to extend variational iteration method and Padeapproximant to solve Glauert-jet problem , known in the Russian literature as the Akatnov results.
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