bbgodfrey

# 11,647 Actions

 25m reviewed Reopen Numeric solution for PD equations with d'Alembert operator 3h reviewed Reopen Transferring a function between two modules in a package 2d reviewed Close WSTP from Wolfram mathematica to nodejs Sep 18 reviewed No Action Needed Extracting the integers from a list Sep 17 reviewed Looks OK rule-based deletions from string list Sep 17 reviewed Close After taking square root of the equation again square root sign is there in the answer after value. Why is it so? Sep 16 comment Shooting Method for Numerical Solution You appear to be trying to integrate along a separatrix, which always is numerically unstable. The best you can do with the shooting method is to integrate along the separatrix for a while, and then stop (say at r == 7). If for some reason you need to integrate further, improve your guess for x'[0.00001]. By the way, the large r solution you obtained is valid, except that it does not match the boundary condition at r == 100, as pointed out by the error messages you received. Sep 16 comment Integral for infinite resistor grid problem The article you sited is wrong, because the integrand is strictly negative. By the way, NIntegrate gives the same answer as Integrate to several significant figures. Sep 16 comment Problems with solving PDEs @user55777 "symbolic asymptotic solution, {(9 - 100 v0)/(-59 + 100 v0), v0}" Sep 16 comment Problems with solving PDEs The first thing to check is whether the equilibrium described near the end of my answer is stable. Do this by linearizing the equations about this equilibrium. Then, Fourier-transform the linearized equations in x Laplace-transform them in t, and determine whether the resulting eigensystem has exponentially growing modes in t. If so, the equilibrium is unstable, and numerical solutions always will blow up in time. If the equilibrium is stable, on the other hand, then the numerical method used by NDSolve must be unstable, and attention should be given to finding a stable algorithm. Sep 15 reviewed Looks OK expression containing radicals of imaginary numbers Sep 14 reviewed Close Fractional order Adams Bash-forth Moulton method Sep 13 comment How do I formulate a Dirichlet boundary condition for which the boundary depends on the other variable? Please provide n[r]. Sep 13 comment Problems with solving PDEs @user55777 I chose 2/5, because it was somewhat larger than the value of v for the initial plateau but still much less than 1. By asymptotic, I meant steady state. The oscillations could be from a physical instability, but they still have to start from some irregularity in x. Because they grow even with c = 0, the only source left is numerical noise. Thanks for checking the spatial derivative terms. Sep 13 comment Problems with solving PDEs @user55777 Yes, I did. However, if WhenEvent is used to terminate the computation before it reaches v == 1, as I did for the fourth and fifth plots, then using Max is unnecessary. By the way, I have some new ideas for investigating the issues here, but I will not have time to do so for a few days. Sep 13 reviewed Reject Finding recurrence formulas from procedural code and output lists associated with integer sequences Sep 12 comment Numerical solution to Differential equation You are changing the question. Please open a new question that includes both the code above and the boundary condition at large r that you are trying to match. My guess is that you are trying to match a separatrix at large r', which typically is difficult but possible numerically. Sep 12 revised Why DSolve gives different answer depending on order of variables: $u(x,t)$ vs. $u(t,x)$? edited tags Sep 12 comment Why DSolve gives different answer depending on order of variables: $u(x,t)$ vs. $u(t,x)$? The sign change shown in the text eliminates the problematic kink in the characteristics. Sep 12 comment Why DSolve gives different answer depending on order of variables: $u(x,t)$ vs. $u(t,x)$? @AlexTrounev Because the PDE is first order in x, only one boundary condition would be needed. And, since the characteristics flow from left to right, as in my second plot, that boundary condition should be on the left. Doing so would not eliminate the strange behavior shown in my answer, unless the boundary condition were at x = 1` or larger.