The practical implementation and efficiency of the numerical methods for solving the Cauchy problem with an algebraic relation between the phase variables

Computational Mathematics and Mathematical Physics, 34(11) (1994), 1389-1401

Two ways of implementing the Adams-Newton method are described. The first involves computing the inverse matrices by Gauss's method, and the second, by Hotelling's method. The practical application of both methods is tested. A combined method, based on the second-order Adams method and a modification of Newton's method, which improves the efficiency of the solution of the Cauchy problem with an algebraic relation between the phase variables, is described.