Parallel algorithm with spectral convergence for nonlinear integro-differential equations

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.

15 pages, 9 figures

References in corpus (2)

• Classical aspects of quantum fields far from equilibrium
• Schwinger-Dyson approach to non-equilibrium classical field theory

Cited by in corpus (3)

• Quantum dynamics of phase transitions in broken symmetry $\lambda {\varphi }^4$ field theory
• Dynamics of broken symmetry lambda phi^4 field theory
• Real-time dynamics of the O(N) model in 1+1 dimensions