Numerical solution of stiff systems of ordinary differential equations by converting them to the form of a Shannon

A new numerical method for solving systems of ordinary differential equations (odes) by reducing them to Shannon equations is considered. To convert differential equations given in Cauchy normal form to Shannon equations, it is sufficient to perform a simple substitution of variables. Nonlinear ode systems are linearized. Piecewise linear approximation of the right-hand sides of the Shannon equations does not require calculations of the Jacobi matrix and provides high accuracy for solving differential equations, including stiff differential equations.