## Central Asian Problems of Modern Science and Education

#### Abstract

Problems of physics, mechanics of theoretical and practical importance are solved by the method of integral equations. Mathematical physics uses integral equations to solve problems. Therefore, it is important to find solutions to integral equations. But it is not always possible to find analytical solutions of integral equations. Thus, we study the numerical methods of integral equations. This paper shows how to find numerical solutions to Volterra equation of the second kind using the MATLAB program. The results are compared with the exact solution by using computer simulations.

#### First Page

51

#### Last Page

59

#### References

[1]. Verlan A.F., Sizikov V.S. Integral equations: methods, algorithms, programs. - Kiev .: Naukova Dumka, 1986. - 544 p. [2]. Manzhirov A.V., Polyanin A.D. Handbook of integral equations: solution methods. M .: Publishing House-Factorial Press, 2000 .- 384 p. [3]. Mikhlin S.G. Lectures on linear integral equations. M .: State publishing house of physical and mathematical literature, 1959. - 232 p. [4]. Bakhvalov N.S. Numerical methods. M .: Publishing house-Naukaa, 1975.636 p. [5]. Glazyrina L.L., Karchevsky M.M. An introduction to numerical methods: a tutorial. - Kazan .: Kazan. un-t, 2012. - 122 p [6]. Krylov V.I. Approximate calculation of integrals. M .: Publishing house-Naukaa, 1967 .-- 500 p. [7]. Mikhlin S.G., Smolitsky H.L. Approximate Solution Methods differential and integral equations. M .: Publishing House Naukaa, 1965 .-- 384 p. [8]. Mikhlin S.G. Variational methods in mathematical physics. M .: Publishing House. Naukaa, 1970 .-- 512 p. [9]. Demidovich B.P., Maron I.A., Shuvalova E.Z. Numerical methods Data analysis. Function approximation, differential and integral equations. M .: Naukaa Publishing House, 1967.368 p. [10]. Bakhvalov N.S. Numerical methods. M .: Naukaa Publishing House, 1975. -632 p.

#### Recommended Citation

Rakhimov, I.D
(2020)
"NUMERICAL SOLUTION OF VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND.,"
*Central Asian Problems of Modern Science and Education*: Vol. 2020
:
Iss.
2
, Article 6.

Available at:
https://uzjournals.edu.uz/capmse/vol2020/iss2/6