Questions tagged [modeling]
Questions about approaches for simulating physical systems or phenomena by building from related understanding and basic principles.
222 questions
6
votes
3
answers
320
views
Incorrect results when solving BVP with 3 non-linear ODEs
This is a build-up question from my previous post.
I am currently having trouble to produce the correct trend using the NDSolve FEM results. I realized that no matter which parameters I changed, the ...
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2
votes
1
answer
140
views
How to write system of 1D non-linear ODEs in inactive form?
I am solving a system of non-constant coefficient, non-linear ODEs, shown as follows:
$$
\frac{\partial}{\partial x} \left[ - B(x) \left( \frac{\partial C_{na}}{\partial x} + C_{na} \frac{\partial y}{\...
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28
votes
4
answers
2k
views
Boids by Simon Woods: can we re-invent further efficient flocking models to forge complexity from simple rules?
It has been 12 years since @simon-woods created this fascinating animation an invented a boids model which is more efficient than typical ones. Code is extremely short an elegant:
...
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1
vote
1
answer
126
views
Local sensitivity analysis (semi-relative)
Can we generate code for semi-relative local sensitivity for an ODE mathematical model?
This is the ODE system I have:
...
- 11
3
votes
2
answers
213
views
Problem with constructing the trajectory of a particle in a pulsating field obtained numerically by solving a wave PDE
I model the propagation of a pulsating wave. Below is a system of partial differential equations with free boundaries (Neumann conditions), as well as a pulsating component.
Individual components of ...
- 2,665
2
votes
1
answer
115
views
How fix error in Mathematica "NDSolve::ndsz: At t == ... step size is effectively zero; singularity or stiff system suspected" when using Manipulate?
I am trying to solve a nonlinear system of differential equations in Wolfram Mathematica using NDSolve and visualize the solution with Manipulate. However, I encounter the following error when running ...
0
votes
2
answers
253
views
How to predict time series?
I have the precipitation of twelve months (t=1,2,...,12) as below.
o = {30, 40, 50, 60, 70, 80, 90, 100, 70, 50, 40, 30};
I have estimated the rainfall using this ...
- 301
1
vote
1
answer
191
views
Is Mathematica enough powerful to simulate turbulence flow around a wing(3D) or a gas turbine blade? [closed]
I was searching and reading something about Mathematica and it was very interesting when realized it can simulate the fluid flow around solids but does anybody succeed to simulate turbulence flow ...
- 143
1
vote
2
answers
213
views
Numerical Stiffness Issue in NDSolve for Stiff ODE System: How to Avoid Extrapolation Errors?
I am trying to solve a stiff system of ode differential equations (ODEs) using NDSolve in Wolfram Mathematica. The problem is related to modeling the dynamics of proteins over time, with parameters ...
2
votes
1
answer
99
views
Unwanted Oscillation in Solution Occurs When Solving Poisson-Nernst-Planck Equation
This is a follow-up post for this question. I am trying to solve the Poisson-Nernst-Planck equation in the form similar to eqns 9 and 10 in this research paper.
Different than the previous question, ...
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1
vote
1
answer
135
views
Singularity error when solving Poisson-Nernst-Planck equation
I am trying to solve the Poisson-Nernst-Planck equation in the form similar to eqns 9 and 10 in this research paper.
To simplify matter, I only consider single ion species ($i=1$) for $\rho_e$, where ...
- 589
2
votes
1
answer
141
views
Fitting data to a system of ODE using ParametricNDSolveValue
I am trying to create the following code to fit data to a system of ODE.
...
- 51
1
vote
0
answers
69
views
How does NDSolve deal with a delay variable [closed]
For a project I'm using an SIR model to simulate a Zika virus outbreak. And I solve a set of differential equations using NDSolve with specific initial conditions. ...
- 11
1
vote
1
answer
258
views
Problem Encountered when Solving a System Consisting of Two PDEs and an ODE in a Semi-NDSolve-based Approach
This is a continuation for question 300522.
Firstly, I have changed the equation for $C_{2\text{b}}^* $ in my system. The updated $C_{2\text{b}}^* $ is expressed as below:
$$
\begin{equation}
C_{2\...
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0
votes
0
answers
130
views
Specifying Prescribed Mesh to Solve for a System Consisting of Two PDEs and an ODE
I am solving the following equations:
$$
\frac{\delta C_{1\text{f}}^*}{\delta t^*} = \frac{\overline{t}}{\overline{x}^2} \frac{\delta}{\delta x^*} \left\{ \mathcal{D} \left[ \frac{\delta C^*_{1\text{f}...
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