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Question: While solving BVP using middefer method, maple produces solution that's not solving my equations. A bug? Please help!

Question:While solving BVP using middefer method, maple produces solution that's not solving my equations. A bug? Please help!

SirKruk 0 Maple
March 18 2012
0

Hello!

I have to  solve following ODE set as a part of my MsC thesisr^2*Hr[r, r]+(r+(1/2)*r^3)*Hr[r]+(r^2-4)*Hr+2*R*(1-exp(-(1/4)*r^2))*Hi-(1/2)*R*r^2*exp(-(1/4)*r^2)*Sii-(1/8)*R*r^4*exp(-(1/4)*r^2) = 0

 r^2*Hi[r, r]+(r+(1/2)*r^3)*Hi[r]+(r^2-4)*Hi-2*R(1-exp(-(1/4)*r^2))*Hr+(1/2)*R*r^2*exp(-(1/4)*r^2)*Sr = 0

r^2*Sr[r, r]+r*Sr[r]-4*Sr+r^2*Hr = 0

r^2*Sii[r, r]+r*Sii[r]-4*Sii+r^2*Hi =0

 

These are linear second order ODEs, for functions Hi, Hr, Sii, Sr with independant variable r. R is known. Equations are stiff in r=0, but this should be no problem using mid-point methods. Or so I'm told. I'm still working on boundary conditions but my current findings are Hi(0) = Hr(0) = Sii(0) = Sr (0)=0 and in r=20 all function equal something small, positive or negative. For details see attached maple sheet.

My problem is, when I take numerical procedures returned by dsolve and plug them back into initial equations, well they do not solve them. This seem to be the case of equations 1 and 3. There are plots of their left-hand-sides:

First equation

 

Third equation 

 

2 and 4 do solve just fine.

I would really appreciate any suggestions or insights about any possible reason of this behavior. And what could I do with it, apart from writing some kind of solver from scratch.

 

 test_sol.mw

 
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