One class of integrals evaluation in magnet solitons theory

Abstract

An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce the calculation of wide class of integrals to a numeric search of integrand denominator roots (in a complex plane) and a subsequent residue calculations. The acceleration of series convergence of residue sum allows to reach the high relative accuracy limited only by roundoff error in case when $10÷15$ terms are taken into account. The circumscribed algorithm is realized in the C program and tested on the example allowing analytical solution. The program was also used to calculate some typical integrals that can not be expressed through elementary functions. In this case the control of calculation accuracy was made by means of one-dimensional numerical integration procedure.