论文标题
非线性透明差异的快速稀疏光谱方法，带有一般内核
A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels
论文作者
论文摘要
我们在对特定的jacobi多项式碱基上作用时，基于Volterra操作员的带状稀疏结构提供了一种基于volterra操作员带的稀疏结构的稀疏光谱方法。该方法不仅限于表格$ k（x，y）= k（x-y）$的卷积型内核，而是以有竞争力的速度和指数收敛的速度为通用内核工作。我们提供各种数值实验，以了解有或没有已知分析解决方案的问题以及与其他方法的比较。
We present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator's banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form $K(x,y)=K(x-y)$ but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments on problems with or without known analytic solutions and comparisons with other methods.
