Finite Differences-Semi discretization method on Heat Equation

Click For Summary
SUMMARY

The forum discussion centers on solving the heat equation using the semi-discretization method with Mathematica 9. The user encounters issues when increasing the variable M (number of steps) beyond 5, leading to performance problems. Another participant clarifies that semi-discretization involves discretizing space while solving time evolution without numerical methods, leveraging Mathematica's capabilities for exact solutions.

PREREQUISITES
  • Understanding of the heat equation and its applications
  • Familiarity with semi-discretization methods in numerical analysis
  • Proficiency in Mathematica 9 for coding and simulations
  • Basic knowledge of boundary and initial conditions in differential equations
NEXT STEPS
  • Explore advanced techniques in Mathematica for optimizing simulations
  • Research MATLAB implementations of the heat equation
  • Learn about numerical methods for time evolution in differential equations
  • Investigate visualization tools for better animation of simulation results
USEFUL FOR

Mathematicians, physicists, and engineers working on heat transfer problems, as well as developers seeking to implement numerical methods in Mathematica or MATLAB.

Juan Carlos
Messages
21
Reaction score
0
Hi!, I'm working on a personal project: Solve the heat equation with the semi discretization method, using my own Mathematica's code, (W. Mathematica 9). The code:
View attachment PDE heat.nb

I'm having problems with the variable M (the number of steps). It works with M=1-5, but no further, I do not know what's going on. Help!
Also, I'm looking for a better animation more intuitive.
Thanks a lot
 
Physics news on Phys.org
Since I do not have mathematica( using MATLAB for simulation purposes) I am just going to ask silly questions :|. As far as a quick google search is concerned Semi discretization means you only discretize space, right? And then you figure out some time evolution method. What are you using for the time evolution?
 
Strum said:
Since I do not have mathematica( using MATLAB for simulation purposes) I am just going to ask silly questions :|. As far as a quick google search is concerned Semi discretization means you only discretize space, right? And then you figure out some time evolution method. What are you using for the time evolution?

Yes, that's the idea of semi discretization(also you can discretize the time or space)- But in this treatment I am working with the spatial variable (discrete), and solving the differential equations of time without any numerical method (certain boundary conditions and initial condition allow me to do it), since mathematica does it exactly.

Did I get you?
Thanks
 

Similar threads

High School Incorporating boundary conditions in the Finite Element Method (FEM)
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Finite Element Method: Weak form to Algebraic Equations?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad 9-point Laplacian stencil derivation
  • · Replies 12 ·
Replies
12
Views
7K
Matlab report help please (Finite Difference Method)
  • · Replies 5 ·
Replies
5
Views
2K
Graduate PDE discretization for semi-infinite boundary?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Crank-Nicholson solution to the cylindrical heat equation
  • · Replies 23 ·
Replies
23
Views
6K
Undergrad Solving 2D Heat Equation w/ FEM & Galerkin Method
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Nonlinear heat equation -- Handling the conductivity
  • · Replies 19 ·
Replies
19
Views
3K
Graduate Finite difference method to solve first-order, multivariable
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Solving Poisson's Equation Using Finite Difference
  • · Replies 1 ·
Replies
1
Views
1K