Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
9
votes
1answer
388 views
How to tell mathematica not to resolve stiffness issues
Very often I solve partial differential equations that are nonlinear and could be up to 4th order. In these cases, it is usual for the solution determined by ...
2
votes
1answer
110 views
ParametricPlot3D doesn't appear
Here I have one simple system solvable with NDSolve. I don't know why ParametricPlot3D doesn't present trajectory in space. I have solutions for x[t], y[t] and z[t]
...
9
votes
1answer
466 views
I failed to solve a set of one-dimension fluid mechanics PDEs with NDSolve
@DNA
The fluid here has been assumed as single component perfect gas i.e. it obeys the equation P=ρRT, the thermal conductivity is assumed as a constant, so the equation is:
...
7
votes
0answers
1k views
Integro-differential equation
I have to numerically solve a nonlinear partial integro-differential equation using Mathematica. This is my equation,
$$\frac{\partial y(x,t)}{\partial t}=\int_{-\infty}^\infty K_0(|x-u|) ...
3
votes
2answers
450 views
optimization problem with NDSolve
I want to minimize the function fcc. When fcc is calculated for a specified point the answer is correct:
...
3
votes
1answer
397 views
NDSolve Problem
I am trying to solve a chemical equilibrium ODE with NDSolve where one function is the argument to another.
I.E. My equations look like:
...
10
votes
3answers
3k views
Plotting a Phase Portrait
I'm trying to plot a phase portrait for the differential equation
$$x'' - (1 - x^2) x' + x = 0.5 \cos(1.1 t)\,.$$
The primes are derivatives with respect to $t$. I've reduced this second order ODE to ...
7
votes
2answers
305 views
How to apply restrictions to the “integrated” variable, when using NDSolve?
I have to integrate an energy along a path. I know the energy at the "beginning" of the path (energy[0]), and I can determine the energy change (gain and loss) ...
10
votes
5answers
995 views
How can you compute Itō Integrals with Mathematica?
How can you compute Itō Integrals with Mathematica? I tried searching through the documentations but I didn't find anything.
P.S. I was not at all sure how to tag this question. I had to put in at ...
5
votes
1answer
353 views
Is it possible to do vector calculus in Mathematica?
I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components ...
3
votes
1answer
475 views
NDSolve with vectors
I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...
3
votes
1answer
602 views
How to discretize a nonlinear PDE fast?
I wish to numerically solve the following PDE. Although there are some complete discussions for solving PDEs in tutorial/NDSolvePDE, there is no hint for the nonlinear case by discretization. Thus, I ...
4
votes
3answers
322 views
How to manipulate gauge theory in Mathematica?
I want to know if there is a way of typing into Mathematica an expression like the following,
$$\epsilon^{\mu \nu \lambda} f^{abc} A^a_\mu A^b_\nu A^c_\lambda + g\epsilon^{\mu \nu \lambda} A^a_\mu ...
3
votes
1answer
246 views
Eliminating functions from system of PDE in Mathematica
Mathematica users,
Let's see an example of three PDEs:
How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
4
votes
1answer
266 views
Using physical dimensions in Mathematica DSolve
I would like to calculate a system of two differential equations in Mathematica using DSolve, like:
...
3
votes
2answers
1k views
Integral equation numerical solution with NDSolve
I'm trying to solve something like: f[x] == Integrate[f[x]*g[x]] where g[x] is known and ...
3
votes
3answers
711 views
DSolve gives complex function although the solution is a real one
I have a problem with the DSolve[] command in mathematica 8. Solving the the following 4th order differential equation spits out a complex solution although it should be a real one. The equation is:
...
2
votes
2answers
287 views
How to solve a Differential Equation with DSolve with Function Coefficient?
Suppose I have
v[x_] = (1.453 Sech[x + 1])^2 + I Sech[x + 1] Tanh[x + 1]
And I have to solve the equation:
...
1
vote
2answers
278 views
Running a Numerical Simulation on a System of Differential Equations with unique initial conditions
I have a system of differential equations as follows:
...
0
votes
1answer
309 views
Solving Differential Equation depending on variables solved by NDSolve
How to solve a differential equation which consists of variables depending upon another differential equation?
21
votes
4answers
545 views
How to use NDSolve to track equilibrium?
I am looking for an extension of NDSolve where integration runs until certain variables are settled at an equilibrium. Now I have a working solution in my sleeves ...
16
votes
2answers
371 views
3D orbits and inaccuracy over time
I wrote a little program to use Newton's Law of Universal Gravitation to animate 3 planets orbiting a central star, but I have run into a problem. Here is the code that I used to create the program (I ...
8
votes
1answer
447 views
Poisson solver using Mathematica
I am looking for some help with a Poisson solver I am writing in Mathematica. The code is quite long with Arrays plugged in, so the full details can be found at http://pastebin.com/uSrSDcW6
I am ...
5
votes
3answers
764 views
NDSolve with Euler method
I want to solve this equation with NDSolve[] using the Euler method:
x'[t] == 0.5*x[t]-0.04*(x[t])^2
with initial condition ...
5
votes
1answer
177 views
Multiple simultaneous events in EventLocator method for NDSolve
I'm using NDSolve to integrate a system of ODEs, and EventLocator to stop the integration when it leaves a certain region in phase space. This works perfectly as it should.
However, I've also added ...
12
votes
3answers
226 views
How to splice together several instances of InterpolatingFunction?
I have a set of InterpolatingFunction returned by NDSolve which are valid over different (but overall continuous) domains. How ...
6
votes
1answer
210 views
NDSolve and WhenEvent Causing Excess Work
When I use the following system
model = {x'[t] == x[t] (1 - x[t]) - x[t] y[t], y'[t] == x[t] y[t] - y[t], x[0] == 0.5, y[0] == 0.5}
with the ...
5
votes
3answers
410 views
How to use results of NDsolve[] for further solving of ODEs?
I have a system of ODEs with 10 eqns. I can solve the first 5 independently. How can I use those results to solve for the remaining 5?
An easy example would be
$\dot{x}=f(x), \quad
\dot{y}=g(x,y)$
...
4
votes
2answers
2k views
How do I solve coupled ordinary differential equations?
I have four coupled ODE's. I am not sure how to plot and solve them using Mathematica.
I won't give the exact problem, but the following is something analogous:
The equations
...
3
votes
1answer
396 views
How do I find the best parameter to fit my data if the model is a interpolating function?
Hi I have a question regarding to find the best parameters for my model to fit my data.
I have 3 ordinary equation, and I now just picked some parameters (...
7
votes
1answer
187 views
What does MaxStepFraction do?
I find that with NDSolve[...] while solving a partial differential equation, changing the MaxStepFraction from ...
6
votes
2answers
421 views
How to set the NDSolve method to LSODA
I notice that off all the Method options available for NDSolve[...], LSODA is invoked quite ...
4
votes
1answer
379 views
Solve system of ordinary differential equations that doesn't have an initial condition (t=0), but has an inifinity condition (t=infinity)?
I have a question for solving t -> Infinity on Mathematica. First, I have a system of ODEs:
...
4
votes
1answer
154 views
Could the PrecisionGoal for NDSolve be a negative number?
The help of Mathematica doesn't say so much about the PrecisionGoal for NDSolve, and I never considered much about it even after ...
2
votes
2answers
259 views
NDSolve: Normalizing at every step
Suppose I have an transport equation with an initial conditions:
...
1
vote
2answers
226 views
NDSolve problems of convergence
I have a big function that I have to maximize, so I have to evaluate some equation with thousands of different values of the parameter.
But the FindMaximum returns me many errors.
I have traced the ...
1
vote
3answers
500 views
How do I plot x[t] vs. x'[t] (where x[t] and x'[t] are solutions to NDSolve)?
I have a differential equation which I solved using NDSolve. I can easily plot x[t] vs. t, x'[t] vs. t, but....
how do I plot x[t] vs. x'[t]?
I tried using the Evaluate function to simplify things, ...
9
votes
1answer
936 views
What method does NDSolve use for solving PDEs?
What is NDSolve's mode of operation?
I use it to solve partial differential equations and never gave it too much thought. Recently, I came across this question. ...
8
votes
1answer
181 views
7
votes
2answers
273 views
Starting NDSolve from intermediate time step?
I always wondered if I could start NDSolve from an intermediate time step.
What I mean is, in the code sample below, if I were to run my solution from tmin=0 to ...
7
votes
1answer
229 views
Setting the DifferenceOrder Option
I've been playing around with Method in NDSolve[...] and can't quite seem to figure out how to force ...
6
votes
0answers
69 views
Return partial result when MemoryConstrained aborts NDSolve
I use NDSolve to solve a large set (~400) of coupled ODEs. Sometimes, the memory (~4GB) gets filled up, and my computer becomes impossible to work with, because it ...
5
votes
4answers
518 views
Change variables in differential expressions
I have a fairly complicated differential expression in terms of a variable r and two unknown functions of r, B[r] and n[r]. I want to do a Taylor expansion of this around r=infinity. I want to do this ...
4
votes
1answer
501 views
Improving NDSolve speed for heavily stiff problems
Having looked around the intergoogles and Mathematica.SE, I thought I'd pose a question with a minimum working example.
Here is the situation I am trying to improve:
I am solving a 4th order non ...
4
votes
1answer
249 views
Solving an ODE numerically
I really appreciate it if anyone helps me with this:
How can I solve this ODE and plot the answer for $x$ on $[0.6,5]$:
$$
\begin{align*}
-2xy'[x] = y''[x]+ 47.21 (-.0025 x^6 & + ...
3
votes
2answers
107 views
Putting NDSolve into ParametricPlot
I am having issues using Manipulate to plot the (numeric) solution to an ODE for different parameter values.
I have a code that has several stages, which seem to ...
3
votes
1answer
394 views
Finding the Minimum value of an interpolating function
I can't seem to use FindMinValue to find the min. value of a curve represented by an interpolating function.
For instance the below code generates an interpolating ...
3
votes
1answer
378 views
MaxSteps and Computing time issue for Solving Differential equation in Mathematica
When we solve differential equation numerically using NDSolve then sometimes we get error like NDSolve::mxst: Maximum steps reached
According to Mathematica docs ...
2
votes
1answer
209 views
Differential equations with jump conditions
Suppose I want to solve an ODE with a DiracDelta source term. In the following example, DSolve does it correctly while ...
2
votes
1answer
328 views
Function output from DSolve
I want to get a function as output form DSolve.
For Example :
sol = DSolve[{Q''[t] + 40 Q'[t] + 625 Q[t] == 100*Cos[10*t], Q[0] == 0, Q'[0] == 0}, Q[t], t]
I ...
