论文标题
用于非局部双曲线偏微分方程的混合HAAR小波搭配方法
A hybrid Haar wavelet collocation method for nonlocal hyperbolic partial differential equations
论文作者
论文摘要
在本文中，我们提出了一种基于有限差和HAAR小波的混合搭配方法，以求解非局部双曲线偏微分方程。由于存在非局部边界条件，开发有效，准确的数值方法来解决此类问题是一项艰巨的任务。该方法的专长是使用给定数据有效地处理积分边界条件。由于HAAR小波的各种有吸引力的特性，例如封闭形式表达，紧凑的支撑和正常值，因此HAAR小波有效地用于空间离散化，而二阶有限差差用于时间离散。已经研究了稳定性和误差估计，以确保该方法的收敛性。最后，将数值结果与几乎没有现有结果进行比较，并且表明通过提出的方法获得的数值结果比现有结果更好。
In this paper, we propose a hybrid collocation method based on finite difference and Haar wavelets to solve nonlocal hyperbolic partial differential equations. Developing an efficient and accurate numerical method to solve such problem is a difficult task due to the presence of nonlocal boundary condition. The speciality of the proposed method is to handle integral boundary condition efficiently using the given data. Due to various attractive properties of Haar wavelets such as closed form expression, compact support and orthonormality, Haar wavelets are efficiently used for spatial discretization and second order finite difference is used for temporal discretization. Stability and error estimates have been investigated in order to ensure the convergence of the method. Finally, numerical results are compared with few existing results and it is shown that numerical results obtained by the proposed method is better than few existing results.
