论文标题
用于分布式订单的多维全局微分方程的计算小波方法
Computational Wavelet Method for Multidimensional Integro-Partial Differential Equation of Distributed Order
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。
This article provides an effective computational algorithm based on Legendre wavelet (LW) and standard tau approach to approximate the solution of multi-dimensional distributed order time-space fractional weakly singular integro-partial differential equation (DOT-SFWSIPDE). To the best of our understanding, the proposed computational algorithm is new and has not been previously applied for solving DOT-SFWSIPDE. The matrix representation of distributed order fractional derivatives, integer order derivatives and weakly singular kernel associated with the integral based on LWare established to find the numerical solutions of the proposed DOT-SFWSIPDE. Moreover, the association of standard tau rule and Legendre-Gauss quadrature (LGQ) techniques along with constructed matrix representation of differential and integral operators diminish DOT-SFWSIPDE into system of linear algebraic equations. Error bounds, convergence analysis, numerical algorithms and also error estimation of the DOT-SFWSIPDE are regorously investigated. For the reliability of the proposed computational algorithm, numerous test examples has been incorporated in the manuscript to ensure the robustness and theoretical results of proposed technique.
