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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >Solving shallow water equations with crisp and uncertain initial conditions
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Solving shallow water equations with crisp and uncertain initial conditions

机译：求解初始条件不稳定且不确定的浅水方程

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Purpose - This paper aims to deal with the application of variational iteration method and homotopy perturbation method (HPM) for solving one dimensional shallow water equations with crisp and fuzzy uncertain initial conditions. Design/methodology/approach - Firstly, the study solved shallow water equations using variational iteration method and HPM with constant basin depth and crisp initial conditions. Further, the study considered uncertain initial conditions in terms of fuzzy numbers, which leads the governing equations to fuzzy shallow water equations. Then using cut and parametric concepts the study converts fuzzy shallow water equations to crisp form. Then, HPM has been used to solve the fuzzy shallow water equations. Findings - Results obtained by both methods HPM and variational iteration method are compared graphically in crisp case. Solution of fuzzy shallow water equations by HPM are presented in the form triangular fuzzy number plots. Originality/value - Shallow water equations with crisp and fuzzy initial conditions have been solved.
机译：目的-本文旨在探讨变分迭代法和同伦摄动法（HPM）在求解具有清晰不确定初始条件的一维浅水方程时的应用。设计/方法/方法-首先，该研究使用变分迭代方法和HPM在盆地深度恒定且初始条件良好的情况下求解浅水方程。此外，该研究从模糊数的角度考虑了不确定的初始条件，这将控制方程推向了模糊浅水方程。然后，使用割和参数化概念，将模糊的浅水方程式转换为清晰的形式。然后，使用HPM求解模糊浅水方程。结果-在清晰的情况下，以图形方式比较了通过HPM方法和变分迭代方法获得的结果。 HPM的模糊浅水方程的求解以三角模糊数图的形式给出。创意/价值-解决了具有脆性和模糊初始条件的浅水方程。

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