Wave eqaution PDE in mathematica

In summary, the wave equation PDE is a second-order linear PDE that describes the propagation of waves in a given medium. To solve it in Mathematica, you can use the built-in function DSolve and specify any necessary boundary or initial conditions. Mathematica can handle non-constant coefficients in the PDE by specifying them as functions of the independent variables. The function Plot3D can be used to visualize the solution of the PDE as a 3D surface. There are various online resources available for learning how to solve the wave equation PDE in Mathematica, such as the official documentation, online forums, and video tutorials.
  • #1
flasherffff
10
0
hi
i can't make DSolve solve the wave equation with simple bvc
ive gone through the mathematica documentation and can't find the answer

for the input


[itex]\text{DSolve}\left[\left\{u^{(2,0)}[x,t]==4 u^{(0,2)}[x,t],u[x,0]==1,u^{(0,1)}[x,0]==\text{Sin}[x]\right\},u,\{x,t\}\right][/itex]
it just return it unevaluated
 
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  • #2
DSolve's ability to deal with PDE's is a little limited. Try solving the PDE without the BCs. This will give a solution in terms of two functions, C[1] and C[2]. Then use the BCs to solve for those.
 

Related to Wave eqaution PDE in mathematica

1. What is the wave equation PDE?

The wave equation PDE (partial differential equation) is a mathematical model that describes the propagation of waves in a given medium. It is a second-order linear PDE that involves both spatial and temporal derivatives.

2. How can I solve the wave equation PDE in Mathematica?

To solve the wave equation PDE in Mathematica, you can use the built-in function DSolve. This function takes the wave equation PDE as an input, along with any necessary boundary or initial conditions, and returns the general solution.

3. Can Mathematica handle non-constant coefficients in the wave equation PDE?

Yes, Mathematica can handle non-constant coefficients in the wave equation PDE. You can use the function DSolve and specify the coefficients as functions of the independent variables.

4. Is there a way to visualize the solution of the wave equation PDE in Mathematica?

Yes, you can use the function Plot3D in Mathematica to visualize the solution of the wave equation PDE. This function allows you to plot the solution as a 3D surface, with one axis representing time and the other two representing the spatial variables.

5. Are there any useful resources for learning how to solve the wave equation PDE in Mathematica?

Yes, there are many online tutorials and resources available for learning how to solve the wave equation PDE in Mathematica. Some recommended resources include the official Mathematica documentation, online forums and communities, and video tutorials on platforms like YouTube.

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