Oops, I should have seen that. Thanks,
-- Raul On Sun, Mar 15, 2015 at 2:45 PM, Kip Murray <[email protected]> wrote: > Raul, where you have _1 * y you need _2 * y > > --Kip > > On Sunday, March 15, 2015, Raul Miller <[email protected]> wrote: > >> On Sat, Mar 14, 2015 at 7:11 AM, Kip Murray <[email protected] >> <javascript:;>> wrote: >> > I recommend a matrix approach involving eigenvalues and eigenvectors, >> > and assume you have a way to find eigenvalues and eigenvectors for an n >> by >> > n matrix which has n linearly independent eigenvectors. I confine my >> > attention to linear differential equations with constant coefficients and >> > right hand side 0, for example >> > >> > u''' - u'' - 4 u' + 4 u = 0 with initial conditions u(0) = 2 , u'(0) = >> _1 >> > , and u''(0) = 5 >> > >> > This has the solution u(t) = ( ^ _2 * t ) + ( ^ t ) where I use a mix >> of >> > conventional and J notation. >> >> I decided to try converting your notes here to J, and I ran into a snag. >> >> First, I tried expressing your initial constraints in J: >> >> constraint=: 1 :0 >> if. 0 = y do. >> assert. 2 = u y >> assert. _1 = u D. 1 y >> assert. 5 = u D. 2 y >> end. >> assert. 0= (u D.3 + (_1*u D.2) + (_4 * u D. 1) + 4 * u) y >> ) >> >> And then I expressed your solution in J: >> >> solution=:3 :0 >> (^ _1 * y) + ^ y >> ) >> >> Or, alternatively: >> >> tacitsolution=: +&^ - >> >> And then I tested my code to see if I had gotten it right: >> >> solution constraint 0 >> |assertion failure >> | _1=u D.1 y >> >> Looking at this: >> solution D.1 (0) >> 9.76996e_8 >> tacitsolution D.1 (0) >> 9.76996e_8 >> >> working this through manually, >> >> dsolution=: 3 :0 >> (_1 * ^ _1*y) + ^ y >> ) >> >> dsolution 0 >> 0 >> >> So J's implementation of D. isn't perfect, but I'm wondering if you >> might not also have a typo somewhere in your presentation here? >> >> Thanks, >> >> -- >> Raul >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > > > -- > Sent from Gmail Mobile > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
