multiple bvp4c?
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From: Rorie Thomson on 3 Jan 2010 07:30 I have 3 nonlinear equations which i need to solve simultaneously using bvp4c. My equations are as follows %Equations % (1) (dT/ds)-T*((8*(pi^2)*y)/(1-4*(pi^2)))*(dy/ds)+2*pi*y*V=0 % (2) (dy/ds)-y_prime=0 % (3) T*(dy_prime/s)+(dT/ds)+(dT/ds)*(dy/ds)-T*4*(pi^2)*y+2*pi*y*S*(dx/ds)+2*pi*y*V*(dy/ds)=0 % (4) (dx/ds)^2+(dy/ds)^2+4*(pi^2)*(y^2)=1 %%%%%%%%%%%%%%%%% The help i have been given so far and have worked out is that it 'should' be possible, i need to solve using bvp4c for each iteration and solve the 4x4 non linear system while using fsolve some how to work out my vaules for dT/ds, dx/ds, dy/ds and dy_prime/ds. Thing is I have no idea how to do this. do i need to run 4 bvp4c files for each part? I can only find bvp4c examples for equations with one differential in them, not 4 like i have. I understand i can use MATLAB to fsolve, but i do this after i have used bvp4c, correct? I have seen that when using bvp4c for a problem such as y''+y=0, i would solve for y'=... and work from there using that equation in the bvp4c solver. I am unsure how i should solve my problem for use in the bvp4c solver (or 4 of them depending ) i have multiple differentials in each equation Thanks!
From: Torsten Hennig on 3 Jan 2010 17:15 > I have 3 nonlinear equations which i need to solve > simultaneously using bvp4c. > > My equations are as follows > > %Equations > % (1) > (dT/ds)-T*((8*(pi^2)*y)/(1-4*(pi^2)))*(dy/ds)+2*pi*y*V > =0 > % (2) (dy/ds)-y_prime=0 > % (3) > T*(dy_prime/s)+(dT/ds)+(dT/ds)*(dy/ds)-T*4*(pi^2)*y+2* > pi*y*S*(dx/ds)+2*pi*y*V*(dy/ds)=0 > % (4) (dx/ds)^2+(dy/ds)^2+4*(pi^2)*(y^2)=1 > %%%%%%%%%%%%%%%%% > > The help i have been given so far and have worked out > is that it 'should' be possible, i need to solve > using bvp4c for each iteration and solve the 4x4 non > linear system while using fsolve some how to work out > my vaules for dT/ds, dx/ds, dy/ds and dy_prime/ds. > Thing is I have no idea how to do this. > > do i need to run 4 bvp4c files for each part? I can > only find bvp4c examples for equations with one > differential in them, not 4 like i have. I understand > i can use MATLAB to fsolve, but i do this after i > have used bvp4c, correct? > > I have seen that when using bvp4c for a problem such > as y''+y=0, i would solve for y'=... and work from > there using that equation in the bvp4c solver. I am > unsure how i should solve my problem for use in the > bvp4c solver (or 4 of them depending ) i have > multiple differentials in each equation > > Thanks! To use bvp4c, you have to supply dy/dx in a separate function (in the examples under http://www.mathworks.com/access/helpdesk/help/techdoc/ref/bvp4c.html this function is called dydx). That's where you have to call fsolve to solve for dT/ds, dy/ds, dy_prime/ds and dx/ds given T, y, yprime and x. By the way: What are the boundary condition for your system of ODEs ? Best wishes Torsten.
From: Torsten Hennig on 3 Jan 2010 17:38 > > I have 3 nonlinear equations which i need to solve > > simultaneously using bvp4c. > > > > My equations are as follows > > > > %Equations > > % (1) > > > (dT/ds)-T*((8*(pi^2)*y)/(1-4*(pi^2)))*(dy/ds)+2*pi*y*V > > > =0 > > % (2) (dy/ds)-y_prime=0 > > % (3) > > > T*(dy_prime/s)+(dT/ds)+(dT/ds)*(dy/ds)-T*4*(pi^2)*y+2* > > > pi*y*S*(dx/ds)+2*pi*y*V*(dy/ds)=0 > > % (4) (dx/ds)^2+(dy/ds)^2+4*(pi^2)*(y^2)=1 > > %%%%%%%%%%%%%%%%% > > > > The help i have been given so far and have worked > out > > is that it 'should' be possible, i need to solve > > using bvp4c for each iteration and solve the 4x4 > non > > linear system while using fsolve some how to work > out > > my vaules for dT/ds, dx/ds, dy/ds and dy_prime/ds. > > Thing is I have no idea how to do this. > > > > do i need to run 4 bvp4c files for each part? I > can > > only find bvp4c examples for equations with one > > differential in them, not 4 like i have. I > understand > > i can use MATLAB to fsolve, but i do this after i > > have used bvp4c, correct? > > > > I have seen that when using bvp4c for a problem > such > > as y''+y=0, i would solve for y'=... and work from > > there using that equation in the bvp4c solver. I > am > > unsure how i should solve my problem for use in > the > > bvp4c solver (or 4 of them depending ) i have > > multiple differentials in each equation > > > > Thanks! > > To use bvp4c, you have to supply dy/dx in a separate > function (in the examples under > > http://www.mathworks.com/access/helpdesk/help/techdoc/ > ref/bvp4c.html > > this function is called dydx). > That's where you have to call fsolve to solve for > dT/ds, dy/ds, dy_prime/ds and dx/ds given T, y, > yprime > and x. > > By the way: What are the boundary condition for your > system of ODEs ? > > Best wishes > Torsten. By the way : in your case, dydx is not a scalar, but a vector of length 4, e.g. if you use the ordering above, dy(1)/dx ~ dT/ds dy(2)/dx ~ dy/ds dy(3)/dx ~ dy_prime/ds dy(4)/dx ~ dx/ds. So you don't have to call bvp4c four times, but you solve simultaneously for y(1), y(2), y(3) and y(4). Best wishes Torsten.
From: Rorie Thomson on 5 Jan 2010 10:01 Thanks, Torsten. I have now managed to set up my ODE side of things. I am struggling a bit with the BC and guess part though. when i am constructing solinit function, and build up my res[ ] with my different points (y(1) to y(4)), how do i fill in things i do not know? for example, if i have y(1)=T, y(2)=y, y(3)=dy/ds and y(4)=x, i have BC that state y=0, x=0, dy/ds=1, but i do not know T. So far i have res = [?; y(2)-1 ; y(3)-1; y(4)-0] Also, i am confused with the set up of it - all the help guides say to use ya and yb, but i do not have these.... an example i found is as follows function res = ex1bc(ya,yb) % as y(1) = u, y(2) = v, y(3) = w, y(4) = z, y(5) = y. res = [ ya(1) - 1 ya(2) - 1 ya(3) - 1 ya(4) + 10 yb(3) - yb(5)]; why do we use ya and yb, and how does this relate to my case? My final question relates to the guess, similarly to above, when i create my function vector, how do i only put in guess' for some bits but not all. In my guess, am i stating that when when y(1)= what ever, y(2) will equal something else stated and so on? Similar to the BC except MATLAB will not always work exactly to this as it is only a guess? If so, can i put in a couple guess'? Thanks again Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <1225666681.12276.1262594352459.JavaMail.root(a)gallium.mathforum.org>... > > > I have 3 nonlinear equations which i need to solve > > > simultaneously using bvp4c. > > > > > > My equations are as follows > > > > > > %Equations > > > % (1) > > > > > (dT/ds)-T*((8*(pi^2)*y)/(1-4*(pi^2)))*(dy/ds)+2*pi*y*V > > > > > =0 > > > % (2) (dy/ds)-y_prime=0 > > > % (3) > > > > > T*(dy_prime/s)+(dT/ds)+(dT/ds)*(dy/ds)-T*4*(pi^2)*y+2* > > > > > pi*y*S*(dx/ds)+2*pi*y*V*(dy/ds)=0 > > > % (4) (dx/ds)^2+(dy/ds)^2+4*(pi^2)*(y^2)=1 > > > %%%%%%%%%%%%%%%%% > > > > > > The help i have been given so far and have worked > > out > > > is that it 'should' be possible, i need to solve > > > using bvp4c for each iteration and solve the 4x4 > > non > > > linear system while using fsolve some how to work > > out > > > my vaules for dT/ds, dx/ds, dy/ds and dy_prime/ds. > > > Thing is I have no idea how to do this. > > > > > > do i need to run 4 bvp4c files for each part? I > > can > > > only find bvp4c examples for equations with one > > > differential in them, not 4 like i have. I > > understand > > > i can use MATLAB to fsolve, but i do this after i > > > have used bvp4c, correct? > > > > > > I have seen that when using bvp4c for a problem > > such > > > as y''+y=0, i would solve for y'=... and work from > > > there using that equation in the bvp4c solver. I > > am > > > unsure how i should solve my problem for use in > > the > > > bvp4c solver (or 4 of them depending ) i have > > > multiple differentials in each equation > > > > > > Thanks! > > > > To use bvp4c, you have to supply dy/dx in a separate > > function (in the examples under > > > > http://www.mathworks.com/access/helpdesk/help/techdoc/ > > ref/bvp4c.html > > > > this function is called dydx). > > That's where you have to call fsolve to solve for > > dT/ds, dy/ds, dy_prime/ds and dx/ds given T, y, > > yprime > > and x. > > > > By the way: What are the boundary condition for your > > system of ODEs ? > > > > Best wishes > > Torsten. > > By the way : in your case, dydx is not a scalar, but a > vector of length 4, e.g. if you use the ordering above, > dy(1)/dx ~ dT/ds > dy(2)/dx ~ dy/ds > dy(3)/dx ~ dy_prime/ds > dy(4)/dx ~ dx/ds. > So you don't have to call bvp4c four times, but you solve > simultaneously for y(1), y(2), y(3) and y(4). > > Best wishes > Torsten.
From: Torsten Hennig on 5 Jan 2010 17:33 > Thanks, Torsten. I have now managed to set up my ODE > side of things. I am struggling a bit with the BC > and guess part though. > > when i am constructing solinit function, and build up > my res[ ] with my different points (y(1) to y(4)), > how do i fill in things i do not know? for example, > if i have y(1)=T, y(2)=y, y(3)=dy/ds and y(4)=x, i > have BC that state y=0, x=0, dy/ds=1, but i do not > know T. So far i have res = [?; y(2)-1 ; y(3)-1; > y(4)-0] > You need four boundary conditions to solve for T, y, y_prime and x. If [s_left;s_right] is the interval of integration, boundary values for the variables can either be given at s_left or s_right. If e.g. T=1 at s_left, you have to specify ya(1)-1.0 in the res-vector, if T=1 at s_right, you have to specify yb(1)-1.0 in the res-vector. The guess for the variables you specify in the solinit routine is arbitrary, but should take into account the boundary values you specified for the variables. If e.g. T=1 at s_left or s_right, the easiest choice for y(1) in the solinit-routine is T=1 on the _whole_ interval [s_left;s_right]. Hope this clarifies your questions. Best wishes Torsten. > Also, i am confused with the set up of it - all the > help guides say to use ya and yb, but i do not have > these.... > > an example i found is as follows > > function res = ex1bc(ya,yb) > % as y(1) = u, y(2) = v, y(3) = w, y(4) = z, y(5) > = y. > res = [ ya(1) - 1 > ya(2) - 1 > ya(3) - 1 > ya(4) + 10 > yb(3) - yb(5)]; > why do we use ya and yb, and how does this relate to > my case? > > My final question relates to the guess, similarly to > above, when i create my function vector, how do i > only put in guess' for some bits but not all. In my > guess, am i stating that when when y(1)= what ever, > y(2) will equal something else stated and so on? > Similar to the BC except MATLAB will not always work > k exactly to this as it is only a guess? If so, can > i put in a couple guess'? > > Thanks again >
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