Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
25
votes
2answers
935 views
Efficient Langevin Equation Solver
This question is not about good algorithms for solving stochastic differential equations. It is about how to implement simple codes in Mathematica efficiently exploiting Mathematica's programming ...
20
votes
4answers
518 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 ...
18
votes
1answer
415 views
Publishing results obtained in Mathematica
I've been using Mathematica to solve nonlinear partial differential equations for my doctoral research for the last 2 years or so. I am not an expert in Mathematica or mathematics and I am an engineer ...
14
votes
3answers
300 views
How to perturb a Dynamic System?
I'm trying to model a basic feedback system with delayed feedback. I've done the initial setup and now want to add a few more advanced features to my system.
Currently, it's just a simple ...
12
votes
3answers
252 views
Accessing Reduce from DSolve
When solving transcendental equations, Solve frequently warns us that inverse functions are being used so that some solutions may not be found.
We also see that ...
12
votes
1answer
311 views
How to guarantee that NDSolve correctly detects abrupt changes in parameters?
When using NDSolve, I often have parameters that, in most of their domain, have a constant or null variation, but that suffer from abrupt variations on a very small ...
12
votes
3answers
204 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 ...
11
votes
1answer
347 views
2D Heat equation: inconsistent boundary and initial conditions
I'm attempting to use NDSolve on a 2D boundary value problem with initial conditions. Upon running my code, I get the following message:
"NDSolve::ibcinc: Warning: Boundary and initial conditions are ...
11
votes
2answers
582 views
How can I solve a difference-differential equation?
How do I ask Mathematica to try to solve a recursive relation that defines a sequence of functions? For example, suppose I know that $g_n(x) = g_{n-1}'(x)$ for $n > 0$ and that $g_0(x) = e^{2x}$. ...
11
votes
1answer
164 views
Optimizing a Numerical Laplace Equation Solver
Laplace's Equation is an equation on a scalar in which, given the value of the scalar on the boundaries (the boundary conditions), one can determine the value of the scalar at any point in the region ...
10
votes
3answers
2k 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 ...
10
votes
5answers
962 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 ...
10
votes
2answers
245 views
DSolve cannot solve for certain branches of the solution
Could somebody please tell me, why I am always getting an error message when trying to run the following code:
...
9
votes
1answer
445 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:
...
9
votes
1answer
587 views
Numerically solving an inhomogeneous partial differential equation
I'm trying to solve a cylindrical partial differential equation with boundary conditions. But I got an error message saying ...
