2002/02/26 by Bogdan Mihaila, Ruth E. Shaw · 5 citations
Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Chebyshev filter #Chebyshev polynomials #Convergence (economics) #Differential equation #Fractional Differential Equations Solutions #Mathematical analysis #Mathematics #Model Reduction and Neural Networks #Nonlinear system #Numerical methods for differential equations #Physics #Spectral method #hep-ph #physics.comp-ph
paper · pdf · doi:10.1088/0305-4470/35/25/311
published in Journal of Physics A Mathematical and General 35(25), 5315-5331 (Institute of Physics) · 15 pages, 9 figures
arxiv created 2002/02/26 · openalex publication_date 2002/06/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.