All Questions
131
questions
1
vote
0
answers
120
views
Iterative PDE solver for 1D Burgers equation
I am looking for an Iterative Numerical PDE solver for 1D Burgers equation. I need to have access to the intermediate solutions of the Numerical Solver. By iterative methods, I mean techniques which ...
- 11
1
vote
2
answers
124
views
Monotonicity of Errors with Respect to Step Sizes in Numerical Methods for PDEs
Consider a non-linear partial differential equation (PDE) (e.g., Burgers' equation) that is solved numerically using a finite difference method (or a similar approach). Suppose a grid search is ...
- 169
0
votes
0
answers
53
views
Prof A. Stanoyevitch's finite difference based PDE matlab code
Where can one find Prof A. Stanoyevitch's finite difference based PDE matlab code? They have a book on such a topic but can't find the accompanying code.
Is it well received? It's not commonly talked ...
- 317
0
votes
1
answer
95
views
Prof Lawrence Shampine's hpde matlab code
Where can one find Prof Lawrence Shampine's hpde matlab code?
Is it well received? It's not commonly talked about.
- 317
2
votes
0
answers
57
views
Why the following discrete inequality are equal?
When reviewing papers on the numerical solutions of Partial Differential Equations (PDEs), I observed the following equation:
$$
(1-C\tau)||\theta^n||^2 \leq ||\theta^{n-1}||^2 + C\tau (h^{2r+2}),
$$
...
- 141
0
votes
0
answers
109
views
Solving a steady-state PDE
I'm working on trying to solve a steady state PDE in python and I am quite new to python and I am slightly confused on the implementation details. I have an example implementation of solving a non-...
- 43
4
votes
1
answer
148
views
Burger's equation (PDE) does not work with downwind difference?
I'm working on implementing the discretised Burger's equation. I am quite confused as to why it does not work when using a step-function and downwind difference formula. When using a step-function and ...
- 43
0
votes
1
answer
68
views
Local truncation error of given implicit 1-step scheme
I'm given the 1-step implicit scheme $$y_{n+1} = y_n + \frac{h}{6}[4f(t_n, y_n) + 2f(t_{n+1}, y_{n+1}) + hf'(t_n, y_n)],$$
where $y'(t) = f(t, y)$, and I'm seeking the scheme's local truncation error. ...
- 1
3
votes
2
answers
279
views
Solving systems of advection-diffusion-reaction equations with finite element methods
I have been doing a lot of self-study on numerically solving PDEs so that I can solve system of linear and nonlinear Advection-Diffusion-Reaction (ADR) systems on complex meshes.
I have been watching ...
- 297
2
votes
1
answer
118
views
How to numerically solve differential equations involving sines, cosines and inverses of the unknown function?
I'm very new to finite difference method and I am just introduced to methods of solving differential equation using finite difference method via sparse matrix method.
I find that the main idea is to ...
- 35
3
votes
1
answer
189
views
Numerical scheme for the level set equation that solves inverse mean curvature flow problems
I am considering the problem of simulating the evolution of an interface given as a curve in 2D (or surface in 3D) that evolves according to a velocity specified at the interface of the form:
$$\vec{v}...
- 33
0
votes
0
answers
64
views
Can I use MOL to solve 2D steady state PDE in terms of r and z spatial coordinates?
recently I need to solve a 2D steady state PDE equation.
It’s not time dependent, and the only two independent variables are z and r direction.
So far for this solution, I was thinking using Method ...
- 1
1
vote
0
answers
102
views
Numerical methods for $u_t+c u_x= \frac{-c}{x}u$?
I am looking for possible numerical methods to solve the PDE
$$u_t+c u_x= \frac{-c}{x}u$$
I am particularly interested in a Finite elements method, although I am also curious if you can expose some ...
- 151
4
votes
1
answer
134
views
A priori FEM estimates without $H^2$ regularity
In basic lectures on finite elements theory, people always assume $H^2$ regularity of the solution in order to derive $O(h^k)$ a priori estimates in the norms $H^{2-k}$, $k=1,2$. For simplicity let's ...
- 259
1
vote
1
answer
150
views
Efficiency of developing PDE solvers using sparse matrices versus loops
I am new to solving PDEs, but have been looking at different implementations of finite difference and finite volume schemes. One thing I have noticed in different implementations is that some ...
- 297