OK, so ive solved a pde numerically. I can plot the solution as a graph, evaluate the value at different times, but how can I integrate it over the region it is defined? My goal is this, the weighted average of x:

I've solved a PDE with pdsolve, I can get the value of u(x,t) at a certain x and a certain t with the value command, K := pds:-value(x = 1-b, t = 0 .. 1, output = listprocedure) leads to; [100.*(x(0) = .99), 100.*(t(0) = 0.), 100.*((u(x, t))(0) = 2.40908278321669992*10^(-93))] id like to get the u(x,t) value out to put it in a function, is there a simple way of doing this? Thanks, Ryan

Hi, I'm working on the Smoluchowski equation (essentially the diffusion eqn with an extra derivative) diff(u(x,t),t)=k*diff(u(x,t),x)+D*diff(u(x,t),x,x) k is piecewise so the function has to be solved numerically, the boundary values are specified u(0,t)=u(1,t)=0 but i need the derivative at the boundaries D[1](0,t) and D[1](1,t). It seems to be simple to evaluate a numeric derivative of an ODE but I can't see how to do it for a PDE. Any help welcome, even some sort of brute force method if necessary. Thanks, Ryan

Hi, I'm working on the Smoluchowski equation (essentially the diffusion eqn with an extra derivative) diff(u(x,t),t)=k*diff(u(x,t),x)+D*diff(u(x,t),x,x) k is piecewise so the function has to be solved numerically, the boundary values are specified u(0,t)=u(1,t)=0 but i need the derivative at the boundaries D[1](0,t) and D[1](1,t). It seems to be simple to evaluate a numeric derivative of an ODE but I can't see how to do it for a PDE. Any help welcome, even some sort of brute force method if necessary. Thanks, Ryan