Re: Solving nonlinear coupled differential equations in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg95332] Re: Solving nonlinear coupled differential equations in Mathematica
- From: Torsten Hennig <Torsten.Hennig at umsicht.fhg.de>
- Date: Thu, 15 Jan 2009 06:14:44 -0500 (EST)
> Here is a set of equations I would like to solve > > y''[x]==y+z'[x] > z[x]^3=y'[x]+3 > > With boundary conditions of y==2 and y==3 > > Using NDSolve on these equations, Mathematica says > the order of the > equations is 3 and it has only 2 initial conditions. > But the order of > this system of equations is 2 as far as I see (since > order is defined > as the highest derivative) > > When I do try to put another boundary condition in > like z==0 > Mathematica spits out that it cant solve for the > derivatives and is > using a mass matrix method (error:ntdvmm) and then it > says that it has > significant errors (error:berr) and will return the > best solution > found. > > Any help on this matter will be greatly appreciated. > Thanks > z^3 = y' + 3 -> 3*z^2*z' = y'' Inserting in the first equation gives 3*z^2*z' = y + z' or z'=y/(3*z^2-1) So you should solve the following two equations (I) z'=y/(3*z^2-1) (II) y'=z^3-3 with appropriate boundary conditions. Best wishes Torsten.