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Parallel algorithm with spectral convergence for nonlinear integro-differential equations

Bogdan Mihaila·Ruth E. Shaw
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Abstract

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.

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Bogdan Mihaila, Ruth E. Shaw. 2002-02-26. Parallel algorithm with spectral convergence for nonlinear integro-differential equations. https://doi.org/10.1088/0305-4470%2F35%2F25%2F311

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