I have developed two models of same scenario. Both models involve a PDE which is solved with same Initial and Boundary conditions. In one model it is solved with Laplace transform and in other with Fourier. After applying both solutions for real field data one model (Fourier transform) is giving a bit different (and queer) results. I have checked all the mathematical steps, coding and field data but could not find a mistake. I don't know this change in results is due to some error by me or the limitation of the method which is used to solve this equation?
2026-03-28 18:01:50.1774720910
Is it possible that a PDE solved by two different analytical methods with same Initial and boundary values give different results?
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There could be several issues here. The first one is rather mathematical: your PDE + initial and boundary conditions could be ill-posed, that is, there could exist multiple solutions. It's not very easy to determine this by looking at the PDE; moreover, for physical applications, this is often regarded as a sign that the model is flawed.
Assuming that your model (PDE + conditions) is well-posed, and should therefore have a unique solution, the second issue could be the numerical implementation of the analytical results. I assume you applied both methods correctly, and that the result you obtained from both is exact. However, the numerical implementation of such expressions is of course never exact. A series gets truncated at a certain order, an integral is approximated using a certain numerical scheme, functions are calculated using a finite size grid, and so on. A famous problem regarding a finite number of terms in a Fourier expansion is the Gibbs phenomenon, which I would classify as 'a bit queer'.
It might be worth it to add a few details to your question, because as it stands, it's not clear how the results you obtain are unexpected.