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Approximate analytical solution for the one-dimensional nonlinear Boussinesq equation

机译：一维非线性Boussinesq方程的近似解析解

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Purpose - The purpose of this paper is to provide closed-form approximate solutions to the one-dimensional Boussinesq equation for a semi-infinite aquifer when the hydraulic head at the source is an arbitrary function of time. Combination of the Laplace transform and homotopy perturbation methods (LTHPM) are considered as an algorithm which converges rapidly to the exact solution of the nonlinear Boussinesq equation. Design/methodology/approach - The authors present the solution of nonlinear Boussinesq equation by combination of Laplace transform and new homotopy perturbation methods. An important property of the proposed method, which is clearly demonstrated in example, is that spectral accuracy is accessible in solving specific nonlinear nonlinear Boussinesq equation which has analytic solution functions. Findings - The authors proposed a combination of Laplace transform method and homotopy perturbation method to solve the one-dimensional Boussinesq equation. The results are found to be in excellent agreement. The results show that the LTNHPM is an effective mathematical tool which can play a very important role in nonlinear sciences. Originality/value - The authors provide closed-form approximate solutions to the one-dimensional Boussinesq equation for a semi-infinite aquifer when the hydraulic head at the source is an arbitrary function of time. In this work combination of Laplace transform and new homotopy perturbation methods (LTNHPM) are considered as an algorithm which converges rapidly to the exact solution of the nonlinear Boussinesq equation.
机译：目的-本文的目的是当源头的水头是时间的任意函数时，为半无限含水层的一维Boussinesq方程提供封闭形式的近似解。拉普拉斯变换和同伦摄动方法（LTHPM）的组合被视为一种算法，可以迅速收敛到非线性Boussinesq方程的精确解。设计/方法/方法-作者结合拉普拉斯变换和新的同伦摄动方法，提出了非线性Boussinesq方程的解决方案。该方法的一个重要特性（在示例中已清楚证明）是，在求解具有解析解功能的特定非线性非线性Boussinesq方程时，可以达到光谱精度。发现-作者提出了Laplace变换方法和同伦摄动方法的组合来求解一维Boussinesq方程。发现结果非常吻合。结果表明，LTNHPM是一种有效的数学工具，可以在非线性科学中发挥非常重要的作用。独创性/价值-当源头的水头是时间的任意函数时，作者为半无限含水层的一维Boussinesq方程提供封闭形式的近似解。在这项工作中，拉普拉斯变换和新的同伦摄动方法（LTNHPM）的组合被视为一种算法，可以迅速收敛到非线性Boussinesq方程的精确解。

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