We study two numerical approximations of solutions of nonlocal diffusion evolution problems which are inspired in algorithms for computing the bilateral denoising filtering of an image, and which are based on functional rearrangements and on the Fourier transform. Apart from the usual time-space discretization, these algorithms also use the discretization of the range of the solution (quantization). We show that the discrete approximations converge to the continuous solution in suitable functional spaces, and provide error estimates. Finally, we present some numerical experiments illustrating the performance of the algorithms, specially focusing in the execution time.
翻译:我们研究两个非本地扩散演变问题解决方案的数值近似值,这些解决方案的灵感来自用于计算图像双边分解过滤的算法,并且基于功能重新排列和Fourier变异。除了通常的时间-空间分解外,这些算法还使用溶解范围的离散(量化 ) 。 我们显示离散近值在合适的功能空间中与连续解决方案相融合,并提供错误估计。 最后,我们提出了一些数字实验,说明算法的性能,特别是执行时间的焦点。