Parallel algorithm with spectral convergence for nonlinear integro-differential equations

We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a linearized version of the problem and a spectral method where unknown functions are expanded in terms of Chebyshev polynomials (El-gendi’s method). This approach is shown to be suitable for the calculation of two-point Green functions required in next to leading order studies of time-dependent quantum field theory. PACS numbers: 02.70.-c,02.30.Mv,02.60.Jh,02.70.Bf,02.60.Nm,02.60.Lj Submitted to: J. Phys. A: Math. Gen. Parallel algorithm with spectral convergence 2