High-Order Multivariate Spectral Algorithms for High-Dimensional Nonlinear Weakly Singular Integral Equations with Delay

One of the open problems in numerical analysis solutions to high-dimensional nonlinear integral equations with memory kernel and proportional delay is how preserve high-order accuracy for nonsmooth solutions. It well-known that these display a typical weak singularity at initial time, which causes challenges developing efficient algorithms. The key idea proposed approach adopt smoothing transformation multivariate spectral collocation method circumvent curse beginning time. Therefore, approximate solution can be tailored exact one, resulting Moreover, we provide framework studying rate convergence algorithm. Finally, give test example show underlying problems.