schrodinger equation and poisson equa...

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Author Message   shi liang (caleb_shi) Member Username: caleb_shi Post Number: 6 Registered: 12-2004 Posted on Wednesday, January 12, 2005 - 07:24 am:    Hi, Sir. last time you said :"FlexPDE uses Newton-Raphson iteration automatically whenever the problem is nonlinear. You don't have to do anything." if we have 2 equations to be solved in flexpde. 1) the schrodinger equation, with V, phi, E 2) poisson equation, with V, phi and E V with boundary specified. Can this be solved automatically by Flexpde? particals in two dimensions Assign_2_rectangular.pde (1.0 k)   Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 304 Registered: 06-2003 Posted on Wednesday, January 12, 2005 - 05:19 pm:    Your script requests an eigenvalue calculation, but the equations are nonlinear. Your term V*Phi requires the product of eigenfunctions. FlexPDE cannot solve nonlinear eigenvalue problems. My remarks about automatic Newton iteration apply only to direct solution of PDE's. The best I can suggest is to solve the PDE system directly, with lamda as a parameter. Use STAGEs and sweep through values of lambda as a parameter study. Solution of a linear eigenvalue problem of similar characteristics might give you a range of lambdas to search.