Abstract
Optimal Variational Iteration Method (OVIM) is Variational Iteration Method (VIM) coupled with auxiliary parameter h. In this paper, we have discussed a hydrological problem with pressure distribution phenomenon solved with Optimal Variational Iteration Method (OVIM). In the framework of Optimal Variational Iteration Method (OVIM), the auxiliary parameter h, that is convergence controlling parameter is the primary tool which guarantees the convergence of said technique. Moreover, the convergence is obtained by so-called residual error method. Results shows that the reliability of the method with the least error and provide the required solution to the pressure distribution of water in a water reservoir in initial four iteration.
Highlights
Differential equations exhibit an extraordinary aptitude to say what will take place in future in the world
The implication of said technique on a partial differential equation shown by equation (8) exhibiting a water flow phenomenon is examined and the results are quite astonishing
From equation (9) to equation (12), there is a gradual increase in the fidelity of solution which eventually results in an approximate solution approaching the exact solution [21]
Summary
Differential equations exhibit an extraordinary aptitude to say what will take place in future in the world. They appear in almost every field, sciences or arts. They can picture of almost every phenomenon of real life. Differential equations can explain our whole life in a systematic way. Differential equations are of two types, Linear and nonlinear one. Most of the phenomenon of sciences and engineering are modeled by nonlinear ordinary and many times partial differential equations. Better and natural approach for the solution is escalating day by day. Nonlinear differential equations are generally very complicated and cannot be resolved accurately. Even if the exact solution is, let say, practicable, there are too many calculations involved, making resulting solution impossible to achieve or challenging to construe
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