NDSolve Mathematica: Solve Diff. Eq. Using Solutions of Another

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Mathematica does not have the capability to numerically solve a differential equation composed of the solutions to another numerical differential equation. This error can be avoided by using the version 7.0 or higher of Mathematica. In summary, it is not possible to numerically solve a differential equation (in Mathematica) that is composed of the solutions to another numerical differential equation in version 6.0. The error can be avoided by using version 7.0 or higher.
  • #1
zeebo17
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Is it possible to numerically solve a differential equation (in Mathematica) that is composed of the solutions to another numerical differential equation such as

Sol1=NDSolve[f'[x]= f[x]...]
Sol2=NDSolve[g'[x]= G( g[x], f[x] )...]

where G(x) is the a function of the interpolating function produced from the previous ODE?

I have tried writing the G(x) as by replacing all the f[x]'s with Evaluate[f[x] /. Sol1] but I get the error
"NDSolve::ndfdmc: Computed derivatives do not have dimensionality \consistent with the initial conditions."

Any suggestions?
Thanks!
 
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  • #2
What version of Mathematica are you using?

Thanks
Matt
 
  • #3
Version 6.0
 

1. What is NDSolve in Mathematica?

NDSolve is a function in Mathematica that is used to numerically solve differential equations. It allows you to input a differential equation along with initial or boundary conditions, and it will provide a numerical solution.

2. How do I use NDSolve in Mathematica to solve a differential equation?

To use NDSolve, you need to first define the differential equation you want to solve using the syntax "eqn = {diffEq, initial/boundary conditions}". Then, use the command "NDSolve[eqn, y, {x, xmin, xmax}]", where "y" is the dependent variable and "x" is the independent variable. The function will return a list of rules that can be used to plot the solution.

3. Can NDSolve in Mathematica be used to solve differential equations using solutions of another equation?

Yes, NDSolve has the option to use the solution of one differential equation as input for another. This can be done by using the syntax "NDSolve[eqn, y, {x, xmin, xmax}, {t, tmin, tmax}]", where "t" is the variable used in the original equation and "eqn" is the differential equation for which the solution is known.

4. Are there any limitations to using NDSolve in Mathematica?

While NDSolve is a powerful tool for solving differential equations, it does have some limitations. It may not be able to find a solution for extremely complex or poorly defined equations. It also has difficulty handling equations with singularities or discontinuities.

5. Can NDSolve in Mathematica be used for systems of differential equations?

Yes, NDSolve can handle systems of differential equations. To use it for this purpose, you need to define the system of equations using the syntax "eqns = {diffEq1, diffEq2, ...}". Then, use the command "NDSolve[eqns, {y1, y2, ...}, {x, xmin, xmax}]". The function will return a list of rules for each dependent variable, which can be used to plot the solutions.

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