3
|
4348 Views
|
5 Replies
|
13 Total Likes
View groups...
Share
GROUPS:

# Nonlinear Partial Differential Equation paid collaboration needed

Posted 1 year ago
 I will pay $200 for the solution of the following nonlinear Partial Differential Equation using Wolfram Technologies: 5 Replies Sort By: Posted 1 year ago Posted 1 year ago  I'm not a expert for solving this kind equation, but using FiniteElement method with coefficient = 3/2, I have:  usol2 = Block[{\[Epsilon] =$MachineEpsilon, inf = 48, coeff = 1 + 1/2}, NDSolveValue[{I* D[M[r, t], t] == (-E^-M[r, t])*(D[M[r, t], r, r] - (D[M[r, t], r])^2 + ( 2 D[M[r, t], r])/r) - NeumannValue[M[r, t], r == \[Epsilon]], DirichletCondition[M[r, t] == coeff*E^(-(r^2/2)), t == 0], DirichletCondition[M[r, t] == 0, r == inf]}, M, {r, \[Epsilon], inf}, {t, 0, 2}, Method -> {"FiniteElement", "InterpolationOrder" -> {M -> 2}, "MeshOptions" -> {"MaxCellMeasure" -> 2/100}}]]; xv = NArgMax[Norm[usol2[0, t]], {t, 1/10, 5/10}]; Show[Plot3D[2 Norm[usol2[r, t]], {r, 0, 3}, {t, 0, 2}, PlotRange -> All, AxesLabel -> {Style["r ", Italic], Style["t", Italic], Rotate["\[LeftBracketingBar]M(r, t)\[RightBracketingBar]", \[Pi]/ 2]}, ViewPoint -> {3, -2.2, 4.1}, MaxRecursion -> 4], ParametricPlot3D[{r, xv, 2 Norm[usol2[r, xv]]}, {r, 0, 3}, PlotStyle -> Directive[Red, Thickness -> 0.005]]] Maybe you post question here ,you got a better answer.Regards M.I.
Posted 1 year ago
 Hello Mariusz Iwaniuk,Thank you for sharing your valuable information with me. I appreciate the time and effort you took to provide them.Regards,Tao Guo
Posted 1 year ago
 Hi @Tao, are you looking for numeric or exact symbolic solution? If numeric, would solutions for large enough (but not infinity) radius suffice as an approximation? If you have any other thoughts or background or references for this problem, it would be very helpful, as well as any initial setup in form of Wolfram Language code that you have may tried already.
Posted 1 year ago
 Hi @Sam, I apologize for the confusion! I realized that I responded to you in the wrong location.