One class of integrals evaluation in magnet soliton theory II

Abstract

The paper proposes an approximate expression for calculating very complex one-dimensional integrals depending on the parameter $a$. These integrals often occur in computational problems theory of magnetic solitons. The resulting analytical expressions are verified by numerical calculation. The comparison shows that the relative accuracy of the approximating expression tends to zero for large and small values of the parameter $a$. In a small region near $a = 0.119$, the error does not exceed five percent, and for parameter values near $18.0$ the relative error does not exceed seven percent. It turned out that the proposed method of constructing approximating expressions can be generalized to much more complex integrals. A program that compares an approximate expression with an exact numerical value written in C and tested on examples that allow analytical solutions.