One class of integrals evaluation in magnet soliton theory II

TL;DR

This paper introduces an approximate analytical method for evaluating complex one-dimensional integrals in magnetic soliton theory, verified by numerical comparisons, with potential for generalization to more complex integrals.

Contribution

It presents a novel approximation technique for complex integrals in magnetic soliton theory, validated through numerical tests and adaptable to more intricate integrals.

Findings

Approximate expressions achieve less than 7% error for key parameter ranges.

Numerical verification confirms the accuracy of the analytical approximations.

Method can be extended to more complex integrals in the field.

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.