Numerical Continuation Method for Nonlinear System of Scalar and Functional Equations

We propose a numerical continuation method for a nonlinear system that consists of scalar and functional equations. At each parameter step, we solve the system by a modified Gauss–Seidel method. An advantage of this method is that the system is divided into two parts and each part is solved by a suitable numerical method with a desired precision. We solve the functional equations self-consistently at each step of the iteration process for the system of scalar equations. We apply the proposed method for calculating temperature dependence of magnetic characteristics of metals in the dynamic spin-fluctuation theory.