NDSolve wave pulse propogation

  • Thread starter FunkyDwarf
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In summary, the speakers are discussing their difficulties with using NDSolve to numerically solve the time evolution of a one-dimensional wave pulse in the time dependent Schrodinger or KG equations. They mention their lack of understanding of the necessary boundary and initial conditions and express their desire to specify an initial form and velocity for the pulse. They suggest reading a book called "Differential equations with Mathematica" for more information on the topic.
  • #1
FunkyDwarf
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Hey guys,

I'm sure I'm doing something really daft in not getting this to work, but...

I want to use NDSolve to numerically solve the time evolution of a (one-dimensional) wave pulse in either the time dependent schrodinger or KG equations. My inability to do so stems from my lack of understanding of what boundary/initial conditions NDSolve wants/needs.

Essentially i'd like to just specify the initial form (gaussian or whatever) and a velocity and watch the thing fly off into the sunset, under what conditions will this occur?

Cheers
-G
 
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  • #2
Dear, i think you have to read few pages from the following book,

"Differential equations with Mathematica" by Martha L. Abell and James P. Braselton.
there is a separate topic with deal with the wave equaiton
you can find it on gigapedia
 

1. What is NDSolve wave pulse propagation?

NDSolve wave pulse propagation is a numerical method used to solve differential equations that model the propagation of wave pulses in a given medium. It involves breaking down the differential equation into smaller, more manageable parts and using mathematical algorithms to solve them iteratively.

2. How does NDSolve wave pulse propagation work?

The NDSolve wave pulse propagation method works by dividing the medium into discrete points and calculating the behavior of the wave pulse at each point over a small time interval. This process is repeated until the wave pulse has propagated through the entire medium.

3. What types of differential equations can NDSolve wave pulse propagation solve?

NDSolve wave pulse propagation can solve a wide range of differential equations, including those that describe wave propagation in various physical systems such as acoustic waves, electromagnetic waves, and seismic waves. It can also handle nonlinear equations and equations with variable coefficients.

4. What are the advantages of using NDSolve wave pulse propagation?

NDSolve wave pulse propagation offers several advantages over analytical methods, including increased accuracy and the ability to handle more complex systems. It also allows for the incorporation of boundary conditions and external forces, making it a versatile tool for studying wave propagation in different scenarios.

5. Are there any limitations to NDSolve wave pulse propagation?

Like any numerical method, NDSolve wave pulse propagation is subject to limitations such as round-off errors and numerical instabilities. It is also computationally intensive and may require significant processing power for complex systems. Additionally, it may not be suitable for solving certain types of equations, such as those with discontinuities or singularities.

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