Let x = (x_1, x_2, .., x_n) be n-dim vector, A_1, A_2,...A_n be symmetric n*n square matrices, B_1, B_2, .., B_n be n-dim vectors and C_1, C_2, .., C_n be scalars.I need to solve the system of ODEsdx_1/dt = (A_1 x, x) + (B_1, x) + C_1dx_2/dt = (A_2 x, x) + (B_2, x) + C_2...................................dx_n/dt = (A_n x, x) + (B_n, x) + C_nwith initial condition, where (A_i x, x) is a quadratic form and (B_i, x) is a scalar product. If n = 2 then it is feasible that a certain linear transform y = Dx + E can "diagonilize" the system, i.e., convert it to 1-dim Riccatti dy_1/dt = a_1*y_1*y_1 + b_1*y_1 + c1, dy_2/dt = a_2*y_2*y_2 + b_2*y_2 + c2. How about n > 2? What robust and stable method would you recommend to do it numerically if analytical solution is impossible? I suppose robust and stable numerical method for 1-dim Riccatti can be generalized for n-dim Riccatti. Can you suggest one?

Check out the paper on Riccati eqns athttp://www4.ncsu.edu/~pfackler/affine/index.htmHTH,matt.

I am with the italian Spelling Police. Please change the name of this thread from 'Riccatti' to the correct 'Riccati'. Thank you.For proof seehttp://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Riccati.html

Thank you for the reference. They recommend the method for n <= 3 and I need it for n >= 3