On one variant of the W-method based on the CROS method

The paper describes a new method based on the one-step Rosenbrock method with complex coefficients (CROS), with an approximate calculation of the inverse matrix using the continuation by the parameter. Numerical differentiation formulas are used to differentiate the Jacobian matrix. The method proposed was tested on a number of nonlinear problems: the Van der Pol system, Van der Pol coupled oscillators, power and exponential tests of N.N. Kalitkin, the lines method for the nonlinear thermal conductivity equation. Since the matrix inversion procedure is replaced by two matrix multiplications, the method can be efficiently implemented on a parallel computer system with a small number of processing units.