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 Nov27 awarded Notable Question Sep24 awarded Autobiographer Jul2 awarded Curious Jan27 awarded Popular Question Jul15 accepted How to solve for $\Gamma(X,t)$ in $\Gamma_{t,X} = S(X,t) \Gamma_X$? Jul15 asked How to solve for $\Gamma(X,t)$ in $\Gamma_{t,X} = S(X,t) \Gamma_X$? Jun24 awarded Teacher Jun11 accepted Determinant of Matrix Computed by Expanding Down the Diagonal? Jun11 comment Determinant of Matrix Computed by Expanding Down the Diagonal? @AndreasBlass I thought the d's were diffusion coefficients but you may be correct -- however, as you say, this would indicate that det(A) is somehow a function of the diagonal entries of A and that doesn't seem correct. Jun11 asked Determinant of Matrix Computed by Expanding Down the Diagonal? May26 answered How do you set up a system of ODE's for this problem? May26 asked Relationship between Turing bifurcation, saddle-node bifurcation, and Hopf bifurcation? May6 comment How to solve partial integro-differential equation? But generally, you're right that initial conditions with dependence on $x$ give interesting behavior more easily and over a wider range of parameter values. However, let me take a look at the particular example I asked about and see if I can find that regime with Turing instabilities. May6 comment How to solve partial integro-differential equation? @rajb245 You're correct in both instances. May6 awarded Commentator May6 comment How to solve partial integro-differential equation? Absolutely fantastic answer. I agree that Runge-Kutta and one of the numerical integration methods you mentioned are most likely the way to go here. Thank you so much for typing this up! From work I've done on a slightly different system, I would expect that there is a range for $u_0$ that gives interesting behavior (due to Turing instability) both with von Neumann b/c and constant initial conditions. At least, this is what I observe for a very similar system (I think only the kinetics differ) described here: math.umn.edu/~ymori/docs/publications/wavepin.pdf May6 accepted How to solve partial integro-differential equation? May5 comment How to solve partial integro-differential equation? Cheers @rajb245 ... if you happen to know how to recast this problem into something that standard numerical methods can handle I would also be very grateful! Also talked to colleagues of mine about the problem and they suggested (i) imposing the integral condition with a Lagrange multiplier (ii) solving the PDE with the integral as new variable $(u_0 - ) = u_i(t)$ so that you get a solution in terms of an integral equation $u(x,t) = h(u_i(t), x, t)$, then solve this integral equation May4 comment How to solve partial integro-differential equation? @rajb245 I hope I clarified your questions with my edits. Also see the reference for the paper where this is from -- I might still miss something in my recount of the problem. May4 revised How to solve partial integro-differential equation? added 215 characters in body