论文标题
基于Taylor和Chebyshev小波方法的抛物线逆问题源识别的比较工作
Comparative work for the source identification in parabolic inverse problem based on Taylor and Chebyshev wavelet methods
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
In this article, we study wavelet collocation methods based on Taylor and Chebyshev wavelets for the source identification in parabolic inverse problem. In the proposed method, highest order derivative is written in terms of Taylor and Chebyshev wavelet series and required unknown terms are obtained using successive integration. Taylor series approximation has been utilized to obtain the source control parameter. Convergence analysis is carried out in order to guarantee the accuracy of the method. Numerical results have been obtained based on the proposed methods and it is shown that Taylor wavelet method provide us better result than the Chebyshev wavelet method. CPU time has also been shown to ensure the efficiency of the method.
