Elimination of uncertainty in solving system of multidimensional differential equations in X for identification of silver nanoparticles on fibers

In the article, an increase of the sensitivity of identification of biologically active metal silver nanoparticles to cancer cells is considered to be based on the results of compiling a system of multidimensional differential equations with respect to X of the ellipses of probabilistic intersection of the spectra of a Raman polarization spectrometer. The nine main peaks of the spectrum of polyester fibers with silver nanoparticles and without them are analyzed with polarization along the X-transverse and Y-along fibers directions. The correlation matrices of the interconnection of peaks of the Raman spectrum are to be introduced into differential equations. During the solution of the system of equations, there is an intersection of the ellipses of the distribution of the statistical data of peak measurements. When checking the solution from the graphical estimation of the intersection of the ellipses of the data distribution of the Raman spectra, there was a 20% error detected in determining the radii of curvature R0 and R1. To eliminate the uncertainty, numerical additive Δ = + 0.34342 is introduced into the differential equation and when solving this system of differential equations with the additive, the accuracy is (-1.42 · 10^-14 ÷ 1.94 · 10^-15) with the radius of curvature R0 = R1 = 3.458112896121225 at a sufficiently high accuracy of 10^-14 (paper)