Article

Numerical solution of nonlinear integro-differential equations

Gulchera ShodmonovaTashkent Institute of Irrigation and Agricultural Mechanization Engineers, 39 Kari Niyazov str., Tashkent, 100000, UzbekistanUtkir IslomovTashkent Institute of Irrigation and Agricultural Mechanization Engineers, 39 Kari Niyazov str., Tashkent, 100000, UzbekistanOtabek AbdisamatovTashkent Institute of Irrigation and Agricultural Mechanization Engineers, 39 Kari Niyazov str., Tashkent, 100000, UzbekistanSanjar KhikmatullaevTashkent Institute of Irrigation and Agricultural Mechanization Engineers, 39 Kari Niyazov str., Tashkent, 100000, UzbekistanUmirzok KholiyorovTashkent Institute of Irrigation and Agricultural Mechanization Engineers, 39 Kari Niyazov str., Tashkent, 100000, UzbekistanShakhnoza KhamraevaTashkent Institute of Irrigation and Agricultural Mechanization Engineers, 39 Kari Niyazov str., Tashkent, 100000, Uzbekistan

IOP Conference Series Materials Science and Engineeringconference2020en

ABI

Abstract

Abstract The paper is devoted to the development of a numerical algorithm for solving nonlinear integro-differential equations based on the use of quadrature formulas. The Koltunov-Rzhanitsyn kernel with weakly singular features of the Abel type is used as a kernel. To conduct a computational experiment, a computer program was developed; the results obtained by this program are reflected in the form of tables and graphs. A test example was solved, and the obtained approximate numerical results were compared with exact solutions. The influence of nonlinearity and integral parts on the nature of oscillatory process of a viscoelastic body was investigated.

Topics

Differential Equations and Numerical Methods Engineering and Agricultural Innovations Structural mechanics and materials

Identifiers

DOI: 10.1088/1757-899x/896/1/012117

Citations and references

Cited by 220 references

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