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  1. CANM, a program for numerical solution of a system of nonlinear equations using the continuous analog of Newton's method

    Abrashkevich, Alexander; Puzynin, I. V.


    equations are often the last step in the solution of practical problems arising in physics and engineering. The purpose of this paper is to present the iterative procedure for finding zeroes of a system of n nonlinear equations in n variables using the continuous analog of Newton's method (CANM). Method of solution: A system of n nonlinear simultaneous equations is solved by the iterative CANM procedure [2-4]. In this approach, the solution of a system F( X)= 0 is reduced to a solution of evolutionary differential equation {d}/{dt }F( X(t))=- F( X(t)), X(0)= X0, with respect to an additional continuous parameter t, 0⩽ tprogram listing for details). The user must also supply subroutine FCN which evaluates the nonlinear functions. The user has the option of either to provide a subroutine JAC which calculates the Jacobian matrix or allow the program to calculate it by the forward-difference approximation. Typical Running time: The running time depends critically upon the number of nonlinear equations to be solved. The test run which accompanies this paper took 0.06 s on the SGI Origin 2000. ReferencesJ.J. Dongarra, J.R. Bunch, C.B. Moler, G.W. Stewart, LINPACK Users' Guide, SIAM, Philadelphia, 1979. These routines are freely available from the NETLIB at M.K. Gavurin, Izv. Vyssh. Uchebn. Zaved. Mat. 5 (1958) 18; M.K. Gavurin, Math. Rev. 25 (1958) 1380; M.K. Gavurin, Uspekhi Mat. Nauk 12 (1957) 173. E.P. Zhidkov, G.I. Makarenko, I.V. Puzynin, Fiz. Èlementar. Chastits i Atom. Yadra 4 (1973) 53; Sov. J. Part. Nucl. 4 (1973) 53. V.S. Melezhik, I.V. Puzynin, T.P. Puzynina, L.N. Somov, J. Comput. Phys. 54 (1984) 221. V.V. Ermakov, N.N. Kalitkin, Zh. Vychisl. Mat. Mat. Fiz. 21 (1981) 491. T. Zhanlav, I.V. Puzynin, Comput. Math. Math. Phys. 32 (1992) 729.