bvp6c

BVP ODE Solver

Description

Kierzenka and Shampine present both theory and implementation of a residual control based BVP solver, commonly known as bvp4c. Presented here is a direct extension to this work, namely development and justification of a sixth-order accurate solver which we have named bvp6c.

Usage should correspond directly with that of bvp4c. Included are examples to both aid this and compare the accuracy of the solvers.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Tutorial on solving BVPs with BVP4C

• MATLAB release: MATLAB 7 (R14)

Other Files

bvp6c/,
bvp6c/bvp6c.m,
bvp6c/bvp6c.m~,
bvp6c/bvp6c_technical_report.pdf,
bvp6c/bvpget.m,
bvp6c/bvpinit.m,
bvp6c/bvpset.m,
bvp6c/CW32/,
bvp6c/CW32/blackbox32.m,
bvp6c/CW32/CW32.m,
bvp6c/CW32/CW32problems.ps,
bvp6c/CW32/CWBVP_data.txt,
bvp6c/CW32/epslist.m,
bvp6c/CW32/make_plots.m,
bvp6c/CW32/problemlist.m,
bvp6c/CW32/results/,
bvp6c/CW32/results/bvp4c.solve.errors0.001.txt,
bvp6c/CW32/results/bvp4c.solve.errors1e-006.txt,
bvp6c/CW32/results/bvp4c.solve.errors1e-009.txt,
bvp6c/CW32/results/bvp4c.solve.errors1e-012.txt,
bvp6c/CW32/results/bvp4c.solve.errors21e-012.txt,
bvp6c/CW32/results/bvp4c_extra.txt,
bvp6c/CW32/results/bvp5c.solve.errors0.001.txt,
bvp6c/CW32/results/bvp5c.solve.errors1e-006.txt,
bvp6c/CW32/results/bvp5c.solve.errors1e-009.txt,
bvp6c/CW32/results/bvp5c.solve.errors1e-012.txt,
bvp6c/CW32/results/bvp6c.solve.errors0.001.txt,
bvp6c/CW32/results/bvp6c.solve.errors1e-006.txt,
bvp6c/CW32/results/bvp6c.solve.errors1e-009.txt,
bvp6c/CW32/results/bvp6c.solve.errors1e-012.txt,
bvp6c/CW32/results/make_plots.m,
bvp6c/CW32/run_CW32.m,
bvp6c/CW32/xlist.m,
bvp6c/deval.m,
bvp6c/examples/,
bvp6c/examples/injection.m,
bvp6c/examples/measles.m,
bvp6c/examples/shockbvp6.m,
bvp6c/ntrp3h.m,
bvp6c/ntrp6c.m,
bvp6c/ntrp6h.m,
bvp6c/odenumjac.m,
bvp6c/readme.txt

[GOUSKOV Alexandre]

 

[Maged Ismail]

Hi,
Great work.
However the file odenumjac.m is missing from this final version. Could you please upload it?

[Nick Hale]

Hi, odenumjac.m is actually part of the MATLAB ode suite, so you should be able to run a search and copy it into the bvp6c folder. However, you're right and this is something that needs fixing, I'll try to do so soon. Thanks for the comment.

[Paul Holland]

Hi

I also think this is an excellent piece of software, so thanks. Just as a note, I needed to copy over ntrp3h.m as well as odenumjac.m to run the examples.

[Nick Hale]

If when using analytic Jacobians you get an error message involving Jip05Jip025 and Jip05Jip075, then copy the following code into lines 1249-1250;

        Jip05Jip025 = Jip05*Jip025;
        Jip05Jip075 = Jip05*Jip075;

Thanks to Maciek for pointing this out

[Artem Korzhenevych]

Hello,
I am sure that there is a typo on the line 486 of bvp6c. This part should read:

if ~isempty(knownPar)
    sol.knownpars = [{knownPar(:)}];
end

Otherwise, Matlab in unable to combine a vector and a structure if these appear to be elements of knownPar.

[Joey Liu]

This package is really good, thanks alot.
However, I do not know that why I encountered with problems when I was using this package.
I did copy m-files to the MATLAB path.
following are messages which MATLAB showed me.
If you can help me, please contact me by the e-mail. I appreciate your kindness very much.

??? Undefined function or method 'odenumjac' for input arguments of type 'function_handle'.

Error in ==> bvp6c>BCnumjac at 1321
[dBCdya,ignored,ignored1,nbc] = odenumjac(@bcaux,bcArgs,bcVal,dBCoptions);

Error in ==> bvp6c>colloc_Jac at 966
    [dGdya,dGdyb,nbc] = BCnumjac(bc,ya,yb,n,npar,nExtraArgs,ExtraArgs);

Error in ==> bvp6c at 346
      [dPHIdy,NF,NBC] = colloc_Jac(n,x,Xmid,Y,Ymid,yp,Fmid,ode,bc,Fjac,BCjac,npar,...

Error in ==> FD_solve at 4
sol2 = bvp6c('ode_file_FD','bc_file_FD',solinit)

[Nick Hale]

Sorry for the confusion. You should save the bvp6c folder somewhere on your system, then in MATLAB select File> Set Path> Add Folder> and then navigate to where you saved bvp6c.

[Qun HAN]

Numerical calculation of the Jacobian consumes must of the computing time. If mex this section, the efficiency can be dramatically improved further.

[Artem Korzhenevych]

Hello,
I wonder if it is possible to use bvp6c with non-autonomous systems, namely in cases where the odefun is changing, depending on the time period. More specifically, I want to solve a two-point BVP, where one of exogenous parameters in ODEFUN changes at a certain time point. Does anyone have experience with this?