sbval

[GeoffD]

Has anyone got an example of successfully getting sbval to work?

I keep getting  : 

I am playing with a 5th-order non-linear system.

Many thanks in advance!

[StuartBruff0]

https://www.mathcadhelp.com/two-point-boundary-value-problems-12591

https://pages.mtu.edu/~tbco/cm3450/bvp.pdf

[GeoffD]

Thanks for the rapid reply - I had already stumbled on the ww.mathcadhelp page (via Google) and this helped provide confidence that I had not completely messed up decoding the sbval documentation. The mtu.edu reference is very good -  it would be great if it could be scooped into Prime documentation to speed things up for future users. I am now happily solving 6th-order highly coupled non-linear differential equations with discontinuous changes in time-dependent coefficients and trying to break things.

Thanks again for the rapid response.

[ttokoro]

[GeoffD]

Thanks ttokoro, this is a nice compact way of solving linear de in Laplace form. Would it work if you had one initial condition - like y(0)=1 and the other boundary condition say y(1)=2 ? 

[LucMeekes]

Yes, but it takes one more (set of) equation(s) to solve.

See attachment.

Success!
Luc

[GeoffD]

Hi LucMeekes,

Fantastic! - I was unaware of this particular move:

- where constraints can be compiled into a vector then solve invoked!

Many Thanks

GeoffD

[ttokoro]

You can solve ant y(t) value. 

[GeoffD]

Hi ttokoro,

Very neat!

Many Thanks

GeoffD

[rgunwaldsen · Accepted solution]

I also have been looking for such an example, and SB_10264300 has provided excellent references.

BVP.pdf is the first reference, and BVD_15.xmcd is implementation of it in MathCad 15. BVD_Prime6 is file converted into Prime 6.

[GeoffD]

Hi, Many thanks for the references - they helped steer me in the right direction. I tried to break sbval using a really tricky D matrix (no idea what it represents)  using: 

Remarkably, sbval found the initial conditions to satisfy boundary conditions - see attached terse worksheet. By playing with additional changes I could switch between - "cannot converge" and my original error message - but it was not clear what was causing the switch. But everyone's help showed me that I was at least using sbval correctly and that the problem resided in my D  matrix somewhere. I finally got sbval working by non-dimensionalizing the differential equations - which may have cleared up an incipient fault with units that I could not see.

Many thanks for the rapid response from everyone! 

[ValeryOchkov]

I use the Odesolve function and the shot method.

[GeoffD]

Hi, Thanks for the response - I got there in the end 🙂

Best Regards

GeoffD

[GeoffD]

Hi ValeryOchko,

I am finding sbval to be working ok now - but before getting there I was able to use solve block constraints to shape the initial conditions of Adams and Rkadapt - but the response was a bit patchy - sometimes it converged and sometimes not, sometimes Find worked and sometimes minimize did. However, when my boundary conditions involve multiple systems states the solve block route seems a reasonable path - however, I have not explored Radau(init, x1, x2, intvls, D, [J], [M], [tol]) where it seems the M matrix can be used to embed functions of states.

Many thanks

GeoffD