Approximate methods for evaluation singular and hypersingular integrals; approximate methoda for solution singular and hypersingular integral equations; theory of approximation; stability of solution of differential equations; numerical methods for solution of direct and inverse tasks of gravity prospect.

Main publications:

I.V. Boykov, Optimal with respect to accuracy methods for evaluation of singular integrals, (in Russian), Saratov State University, Saratov, 1983

I.V. Boykov, Approximate methods for solution of singular integral equations, (in Russian), Penza State University, Penza, 2004

I.V. Boykov, Approximate methods of evaluation singular and hypersingular integrals. Part 1. Singular integrals. Part 2. Hypersingular integrals, (in Russian), Penza State University, Penza, 2005, 2009

I.V. Boykov, Optimal methods for approximation functions and evaluation integrals, (in Russian), Penza State University, Penza, 2007

I.V. Boykov, Stability of solution of differential equations, (in Russian), Penza State University, Penza, 2008