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：我们研究了非局部扩散演化问题解的两种数值逼近方法，这些方法受图像双边去噪滤波算法的启发，基于函数重排和傅里叶变换。除通常的时空离散化外，这些算法还使用了解的值域离散化（量化）。我们证明了在适当函数空间中离散逼近收敛到连续解，并给出了误差估计。最后，我们通过数值实验展示了算法的性能，特别关注执行时间。