Numerical solution of a certain type of integral equations on the real half-line

2008/09/12 by S. A. Belbas, Belbas, S. A.
Mathematics · Physics and Astronomy · #45G1 #45J05 #65H10 #65J10 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.0809.2125

openalex publication_date 2008/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the convergence and the rate of convergence of our method. The discretization results in an infinite-dimensional nonlinear system, and we also prove results on the approximation of the solution of the infinite-dimensional system by solution of finite truncations.

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