Solver for Partial Differential Equations

FlexPDE is a scripted finite element model builder and numerical solver. The software is available @ http://www.flexpde.com/sdmenu5.html

and a Student License @ http://www.flexpde.com/student5.html

and sample books @ http://www.flexpde.com/bookstore.html


Consider solving the following PDE problem with the specified boundary conditions:


You have to develop the script first.

FlexPDE equations must be second order or less in space and first order or less in time, so one has to split this equation into a system of three equations:

w: dt(w)=u
v: dxx(w)=v
u: EI*dxx(v)+rho*A*dt(u)=0

Now for the boundary conditions

w=0 is a boundary condition on w,
dxx(w)=0 is boundary condition on v,
dxx(w)=M/EI is boundary condition on v,

and

EI*dx(v)=EI*dxxx(w)=F is the natural BC for the u equation.