Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations
Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations
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DOI：
10.1080/17415977.2016.1240793
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发表时间：
2017-01-01
影响因子：
1.3
通讯作者：
Laleg-Kirati, Taous-Meriem
中科院分区：
文献类型：
--
作者：
Asiri, Sharefa;Laleg-Kirati, Taous-Meriem
本文提出了一种基于调制函数的一维偏微分方程时空相关未知量估计方法。该方法将该问题简化为参数未知的线性代数方程组。证明了基于调制函数的解的适定性。以波和五阶KdV方程为例，验证了该方法在无噪声和有噪声情况下的有效性。
In this paper, modulating functions-based method is proposed for estimating space-time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear in unknown parameters. The well-posedness of the modulating functions-based solution is proved. The wave and the fifth-order KdV equations are used as examples to show the effectiveness of the proposed method in both noise-free and noisy cases.