Language: Fortran

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CONTIN-NLIN is the program for numerical continuation of solutions of the following system of two nonlinear ODEs:

u₁"(x)+F₁₁(u₁,u₂,x,)u₁'(x)+F₁₂(u₁,u₂,x,)u₂'(x)+G₁(u₁,u₂,x,) = 0 ,
u₂"(x)+F₂₁(u₁,u₂,x,)u₁'(x)+F₂₂(u₁,u₂,x,)u₂'(x)+G₂(u₁,u₂,x,) = 0 ,

where axb, - vector of parameters, F_ij and G_i (i,j=1,2) - given functions, solution is continued in one of elements of vector , boundary conditions have the following form:

D_i*u_i'(a) + Q_i*u_i(a) = 0,      DD_i*u_i'(b) + QQ_i*u_i(b) = 0.
Here i=1,2, D_i² + Q_i² > 0,     DD_i² + QQ_i² > 0.

The continuation scheme through turning points is described in [1]. At each step of numerical continuation, the Newtonian iteration scheme [2] with the 4th accuracy finite-difference approximation [3] is used.

Sources, tests and the detailed description (in Russian, pdf) are submitted.

References:

1. E.V.Zemlyanaya, I.V.Barashenkov. Mathematical Modeling. V.16, No.10,
   pp.3-14, 2004.
2. I.V.Puzynin, I.V.Amirkhanov, E.V.Zemlyanaya et al. Particles & Nuclei.
   v.30, No.1, pp.210-265, 1999.
3. E.V.Zemlyanaya, I.V.Puzynin, T.P.Puzynina. JINR Comm. P11-97-414, Dubna,
   1997.

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