How is Finite Difference Method?

In summary, the conversation discusses a finite difference linear and non-linear PDE course that the speaker will be taking next semester. They express their curiosity about the enjoyment and difficulty of the material, as well as their preference for projects over tests. The speaker also mentions their previous experience with finite element method and analytical problem-solving in a PDE course. They express some anxiety about learning the FDM method, but it is noted that it is a popular and relatively easy method. The other person in the conversation encourages the speaker to enjoy the course and offers to learn from any problems they encounter.
  • #1
womfalcs3
62
5
I'm going to take a finite difference linear and non-linear PDE course next semester. I'm wondering how enjoyable the material is, and how difficult it may be. I'm actually looking forward to the fact there may only be one test throughout the semester, if any, and it's a mid-term. The rest of the course are homeworks and projects. When I have a lot of time, I can usually figure things out, so I like projects over tests.



I've taken finite element method before in solving linear ODE's. So it'd be good if both methods are compared.

I have also taken a PDE course in which the problem-solving was analytical, rather than numerical. So my anxiousness is derived from the FDM method implementation, and not the PDE's themselves.
 
Physics news on Phys.org
  • #2
It seem that Finite Difference Method is quite a popular method for approximating pde solution. Probably it is the easiest method. I haven't learn it before. But I have seen people using the method.

I think you wouldn't have any problem with the method since you have already learned FEM (I also haven't learn this. All this while have been solving analytically.)

So enjoy the course and write to this forum if you have any problem! May be I could learn something from it :wink:
 

1. What is the Finite Difference Method?

The Finite Difference Method is a numerical method used to solve differential equations. It involves dividing the domain into a finite number of grid points and approximating the derivatives at those points using the values of the function at neighboring points.

2. How does the Finite Difference Method work?

The Finite Difference Method works by approximating the derivatives of a function at a specific point using the values of the function at neighboring points. This is done by using Taylor series expansions and truncating the series at a specific order. The resulting system of equations can then be solved to obtain the values of the function at each grid point.

3. What are the advantages of using the Finite Difference Method?

The Finite Difference Method is relatively easy to implement and can handle complex geometries and boundary conditions. It is also a versatile method that can be applied to a wide range of differential equations, including both linear and nonlinear equations.

4. What are the limitations of the Finite Difference Method?

One limitation of the Finite Difference Method is that it can only approximate derivatives at discrete points, which may result in errors. Also, the accuracy of the method depends on the grid spacing, with smaller grid spacing leading to more accurate results. In addition, the method may become computationally expensive for problems with a large number of grid points.

5. How is the Finite Difference Method different from other numerical methods?

The Finite Difference Method differs from other numerical methods, such as the Finite Element Method and the Finite Volume Method, in the way it approximates derivatives. The Finite Element Method and the Finite Volume Method use piecewise polynomial functions to approximate the solution, while the Finite Difference Method uses a finite difference approximation of the derivatives. Each method has its own advantages and limitations, and the choice of method depends on the specific problem at hand.

Similar threads

B Incorporating boundary conditions in the Finite Element Method (FEM)
    • Differential Equations
Replies
4
Views
753
Finite difference method nonlinear PDE
    • Differential Equations
Replies
2
Views
2K
I Finding the weak form of an eq. with DG elements (finite elements)
    • Differential Equations
Replies
6
Views
2K
MHB Matrix Methods for Difference Problems
    • Differential Equations
Replies
3
Views
2K
I Boundary Conditions For Modelling of a Fluid Using Euler's Equations
    • Differential Equations
Replies
16
Views
2K
A 2D Finite Difference formulation in polar coordinates.
    • Differential Equations
Replies
4
Views
4K
A 2D Finite Difference Convergence Rate Issues
    • Differential Equations
Replies
1
Views
1K
I Numerical solution to the Schrodinger eqn. using Finite Difference Method
    • Quantum Physics
Replies
1
Views
959
Poisson PDE in polar coordinates with FDM
    • Differential Equations
Replies
2
Views
3K
Finite difference method for the diffusion-advection equation
    • Calculus and Beyond Homework Help
Replies
7
Views
1K

Hot Threads

Recent Insights

Back
Top