Differential Equation and Mathematica

In summary, Mathematica can numerically solve second order differential equations and the NDSolve function should be used. The differential equation can be solved using the initial conditions u_i(0)=-i and u'_i(0)=0. The syntax for NDSolve can be found in the help browser of Mathematica or through the Mathematica newsgroup. Graphing the numerical solutions can also be done using the NDSolve function.
  • #1
b2386
35
0
Hi all,

Does anyone know if Mathematica can numerically solve a second order differential equation?
 
Physics news on Phys.org
  • #2
Sure can. Look up NDSolve.
 
  • #3
Well, I have been trying to solve this equation with mathematica for the past two hours with no luck.

The general differential equation I am trying to solve is [tex]u''_i(T) = .65\frac{u'_{i-1}(T)-u'_{i}(T)}{u_{i-1}(T)-u_{i}(T)}+750(u_{i-1}(T)-u_{i}(T)-1)^3[/tex] where i= 1,2,3 and [tex]u'_0(T)=2\pi*Sin(2*\pi*T)[/tex]

The initial conditions are [tex]u_i(0)=-i[/tex] and [tex]u'_i(0)=0[/tex]. I tried using NDSolve but it kept saying that the input was not a differential equation. Does anyone know what should be the syntax of the NDSolve function I need?
 
Last edited:
  • #4
Well, I finally was able to get the NDSolve to work for this differential equation for T values from 0 to 24 and I set the NDSolve function to the variable "soln". So what function should I use to graph the numerical solutions?
 
  • #5
b2386 said:
So what function should I use to graph the numerical solutions?
Look into the help browser of Mathematica (press F1) under NDSolve. There should be a list of examples (see 'Further examples'). From this you will also see how to plot the solution provided by NDSolve. See also http://documents.wolfram.com/mathematica/Built-inFunctions/NumericalComputation/EquationSolving/FurtherExamples/NDSolve.html [Broken].

Finally, I should point out, that this question really belongs in the Mathematica newsgroup, found through Google Groups.
 
Last edited by a moderator:

What is a differential equation?

A differential equation is a mathematical equation that describes a relationship between a function and its derivatives. It is used to model change over time or space, and is commonly used in fields such as physics, engineering, and economics.

How can Mathematica be used to solve differential equations?

Mathematica is a computational software program that can solve differential equations numerically and symbolically. It has built-in functions specifically designed for solving differential equations, and also allows for user-defined functions and equations to be inputted.

What are the advantages of using Mathematica for solving differential equations?

Mathematica offers a wide range of numerical and symbolic methods for solving differential equations, making it a versatile tool for different types of problems. It also has advanced visualization capabilities, allowing for the graphical representation of solutions. Additionally, Mathematica has a user-friendly interface and offers detailed documentation and support.

Can Mathematica handle systems of differential equations?

Yes, Mathematica has the capability to solve systems of differential equations, which are equations that involve multiple functions and their derivatives. It can also handle higher-order differential equations, which involve higher derivatives of a function.

Are there any limitations to using Mathematica for differential equations?

While Mathematica is a powerful tool for solving differential equations, it may encounter difficulties with certain types of equations that require advanced mathematical techniques. In these cases, it may be necessary to use other software or manual methods to find a solution.

Similar threads

  • MATLAB, Maple, Mathematica, LaTeX
Replies
4
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
4
Views
358
  • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
1K
Replies
3
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
3
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
5
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
203
  • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
6
Views
2K
Back
Top