Mathematics

Numerical method for solving scalar problem of monochromatic wave scattering from a screen with nonlinear transmission conditions

V. O. Nesterov, A. A. Tsupak

Penza State University, Penza

Abstract: Background. The purpose of the study is to develop a numerical approach for solving the scalar diffraction problem on a flat screen with nonlinear transmission conditions. Material and methods. The original problem is reduced to a weakly singular nonlinear integral equation; the collocation method is used to solve the integral equation. Results. The diffraction problem is reduced to a nonlinear integral equation over the screen surface; a numerical method was developed for approximate solving the integral equation. Conclusions. An efficient convergent numerical method was developed and implemented to solve the actual diffraction problem.

Keywords: scalar diffraction problem, nonlinear integral equation, collocation method, iterative procedure

UDC: 517.968

DOI: 10.21685/2072-3040-2025-3-2