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