| Author | Message | ||
     Dave (windtornocean) New member Username: windtornocean Post Number: 1 Registered: 04-2006 |
If solving a set of three PDEs for A(x), B(x), and C(x) simultaneously in 1-D, where 2nd derivatives with x of each of A, B, and C are involved, and where A, B, and C are coupled by nonlinear expressions that are specified in the definitions section, can one expect FLEXPDE to have a chance of finding the correct solution regardless of the degree of nonlinearity in the expressions that couple A, B, and C, as long as the initial guesses are "good enough"? Or is it known that a system of three nonlinearly coupled PDE's involving 2nd derivatives will generally cause FlexPDE to fail to converge or to produce unreliable solutions, even in 1-D? I ask because the help information in another software package warns that solutions of some coupled PDE's (Laplace equation in x and y) with second derivatives is not possible because they use a numerical method of lines approach. The Laplace equation is not the same type of PDE as the one that I have described, but the warning from the other software vendor has me wondering if there is a published list of the classes of PDE's for which FlexPDE is known to be unreliable, or if someone happens to know off hand if the class of problem that I have described above is beyond the capability of FlexPDE. Dave | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 585 Registered: 06-2003 |
FlexPDE regularly solves highly nonlinear coupled systems. It uses the Finite Element method, with simultaneous solution of Newton's method for all nodal variables. Adaptive time steps allow FlexPDE to respond to the actual time scale of events and guarantee convergence and accuracy. Shortcomings of other products are not good indicators of the capabilities of FlexPDE. See the example problems: "Samples | Time_Dependent | Chemistry | Chemburn.pde", which calculates explosive chemical reactions in a combustion tube. "Samples | Time_Dependent | Chemistry | Melting.pde", which calculates the solid/liquid phase transition of a metal, including latent heat. "Samples | Steady_State | Chemistry | Reaction.pde", another nonlinear chemical reaction system. |