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

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