I'm guessing that nothing changes in terms of the difficulty of literally solving these problems numerically, but that the difficulty here refers to the ease of getting efficient and stable/high quality integrations -- Maybe that would necessitate using more sophisticated approximations and mathematical restatements to make problems more amenable to numerical integration?
djevans
Is there any relationship between the Laplacian and the Laplace transform. I feel like I remember doing heat transfer problems with Laplace transforms, but I can't remember the specifics.
keenan
@zpb The difficulty is all about the difficulty of solving them numerically (stability, accuracy, etc.). These almost always translate directly to more computational effort. So it's not just a matter of "thinking harder"; it really does come down to more time steps, finer grids, more nonlinear equations to solve, etc.
I'm guessing that nothing changes in terms of the difficulty of literally solving these problems numerically, but that the difficulty here refers to the ease of getting efficient and stable/high quality integrations -- Maybe that would necessitate using more sophisticated approximations and mathematical restatements to make problems more amenable to numerical integration?
Is there any relationship between the Laplacian and the Laplace transform. I feel like I remember doing heat transfer problems with Laplace transforms, but I can't remember the specifics.
@zpb The difficulty is all about the difficulty of solving them numerically (stability, accuracy, etc.). These almost always translate directly to more computational effort. So it's not just a matter of "thinking harder"; it really does come down to more time steps, finer grids, more nonlinear equations to solve, etc.