A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels

We present a sparse spectral method for nonlinear integro-differential Volterra equations based on the operator's banded sparsity structure when acting specific Jacobi polynomial bases. The is not restricted to convolution-type kernels of form $K(x,y)=K(x-y)$ but instead works general at competitive speeds and with exponential convergence. provide various numerical experiments problems or without known analytic solutions comparisons other methods.