Solve the following problem with boundary condition using version 11.01.?

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 claygruesbeck 1 Vote I get error messages when attempting to solve this problem It is easily solved if the conduction term (D[c[z, r], z, z]) and the corresponding boundary condition ( (D[c[z, r], z] /. z -> 1) == 0 )are removed ,however it needs the conduction term in the system I want to simulate eqns = { (1 - r^2) r D[c[z, r], z] == 0.1 (r D[c[z, r], r, r] + D[c[z, r], r] + D[c[z, r], z, z]) - 0.01 c[z, r], c[0, r] == 0, (D[c[z, r], r] /. r -> 10^-6) == 0, c[z, 0.999] == 1 - Exp[-1000 z^2], (D[c[z, r], z] /. z -> 1) == 0}; u = NDSolveValue[eqns, c, {z, 0, 1}, {r, 10^-6, 0.999}] Plot3D[u[z, r], {z, 0, 1}, {r, 10^-6, 0.999}, PlotRange -> {0, 1}] 
1 year ago
5 Replies
 At least in version 10.1, if I start a fresh MMA session and immediately evaluate this eqns = {(1-r^2) r D[c[z,r],z]==0.1(r D[c[z,r],r,r]+D[c[z,r],r]+D[c[z,r],z,z])-0.01 c[z,r], c[0,r] == 0, (D[c[z, r], r] /. r -> 10^-6) == 0, c[z, 0.999] == 1 - Exp[-1000 z^2], (D[c[z, r], z] /. z -> 1) == 0}; u = NDSolveValue[eqns, c, {z, 0, 1}, {r, 10^-6, 0.999}]; Plot3D[u[z, r], {z, 0, 1}, {r, 10^-6, 0.999}, PlotRange -> {0, 1}] then without warning or error it displays
1 year ago
 Thank you Bill, in version 11, I get the following messages when I evaluate the same code. CoefficientArrays::poly: (c^(0,1))[z,1/1000000] is not a polynomial. DirichletCondition[(c^(0,1))[z,1/1000000]==0,r==1.*10^-6] needs to be \ linear 
 Does the problem persist with this modification eqns = {(1-r^2) r D[c[z,r],z]==1/10(r D[c[z,r],r,r]+D[c[z,r],r]+D[c[z,r],z,z])-1/100 c[z,r],c[0,r]==0, (D[c[z, r], r] /. r -> 0) == 0, c[z, 1] == 1, (D[c[z, r], z] /. z -> 1) == 0}; u = NDSolveValue[eqns, c, {z, 0, 1}, {r, 0, 1}] No. That doesn't appear to work either. And neither does this eqns = {(1-r^2) r D[c[z,r],z]==1/10(r D[c[z,r],r,r]+D[c[z,r],r]+D[c[z,r],z,z])-1/100 c[z,r], c[0,r]==0, Derivative[0, 1][c][z, 0] == 0, c[z, 1] == 1, Derivative[1, 0][c][1, r] == 0}; u = NDSolveValue[eqns, c, {z, 0, 1}, {r, 0, 1}] So I've exhausted my tips. Sorry. Hopefully someone better will be able to see what you need to do.