Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

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5
votes
2answers
433 views

StreamPlot for Bifurcation Diagram

When we do a StreamPlot, I want to show the bifurcation when $a = 0$ transitions to $a >0$, but do not see a better way to do this than the following. ...
5
votes
1answer
285 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
1answer
387 views

Using physical dimensions in Mathematica DSolve

I would like to calculate a system of two differential equations in Mathematica using DSolve, like: ...
5
votes
3answers
403 views

Solving recurrence sequence using an ODE

I'm trying to solve the recurrence a[n] == 0 for n < l a[l] == 1 a[n] == (l + 2(n - l) a[n - l] + (n - l)(n - 1) a[n - 1])/n(n - l + 1) for n >= l using ...
5
votes
2answers
226 views

Manipulation of InterpolatingFunction

Suppose that $q[t]$ is obtained by NDSolve as an InterpolatingFunction, and I want to define $Q[t]$ to be some function of ...
5
votes
1answer
320 views

Only final result from NDSolve

Finally I started to play with differential equations in Mathematica. And I have faced the problem, which seems too me so basic that I'm afraid this question is going to be closed soon. However, ...
5
votes
1answer
242 views

How do I interpret an error message from DSolve?

I am trying to find non-trivial solutions of the ODE $\lambda u'(x) = u(x+R) - u(x)$ using Mathematica. In particular, I am using the command ...
5
votes
1answer
209 views

Optimizing Monte Carlo simulation of a Pred-Prey model

My assignment and code As part of an assignment for one of my classes, I'm trying to run a "massive" Monte Carlo simulation in Parallel on the follow model: ...
5
votes
2answers
85 views

Customizing display of partial differential equations

I am manipulating partial differential equations symbolically, and would like to get the easily readable form $\rho \frac{\partial v}{\partial t}$, leaving variables implicit. Based on suggestions ...
5
votes
1answer
94 views
5
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2answers
79 views

Automatically detect largest interval over which NDSolve can find a solution

Question: Consider the following numerical resolution: NDSolve[eqn, {x1[t], x2[t], y[t]}, {t, tmin, tmax} where eqn, ...
5
votes
1answer
308 views

Detecting a collision in n-body simulation with NDSolve

Consider this three-body system: ...
5
votes
1answer
472 views

Unexpected results from NDSolve

I am trying to solve a stiff reaction diffusion system with NDSolve. However, it does not produce the expected results. My problem is a spherical cell with 5 ...
5
votes
1answer
197 views

VariationalD giving the wrong solution?

EDIT: As pointed out in the comments, VariationalD gives a variational derivative (which I don't want), not a derivative with respect to a function (i.e. ...
5
votes
1answer
820 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: ...
5
votes
1answer
144 views

Set some Method options for NDSolve globally while allowing others to change

In a code base that is difficult to change for unrelated issues, I have many invocations of NDSolve that look like the following: ...
5
votes
1answer
122 views
5
votes
0answers
210 views

NDSolve and memory usage

After some googling, i've found similar problems around, but didn't find a 100% satisfactory answer, so let me ask here: I'd like to solve a 1+1 problem using the method of lines. In spherical ...
5
votes
0answers
118 views

Numerical solution of Schrödinger-type equation in Mathematica [duplicate]

I want to solve the following differential equation numerically: \begin{equation} i\partial_{t}\psi(r,t)=\left[-\frac{\Delta}{2m}+g\left|\psi(r,t)\right|^{2}+V_{d}(r,t)\right]\psi(r,t) \end{equation} ...
5
votes
0answers
86 views

Modify NDSolve`StateData (if possible)

I am trying to solve a PDE that needs to be scaled constantly (refer to this). @andre suggests I modify NDSolve`StateData. Now, the problem is, I'm not used to ...
5
votes
0answers
344 views

Modeling neural excitation with a non-linear differential equation

I think I have a special problem and I am not sure how to search for an answer, so I thought I would try here. I am working with the so called FitzHugh-Nagumo model which describes very simple ...
5
votes
0answers
221 views

Second-Order Feedback Pathways

I'm relatively new to Mathematica and I've tried searching and reading through the Mathematica documentation but I'm not able to find a good place to start. I want to model a simple, second-order ...
4
votes
2answers
681 views

Does Mathematica have a command analogous to ode45 of MATLAB?

Does anybody know if Mathematica has an analogue of MATLAB's ode45 command? I need to solve a second order coupled ODE system of equations.
4
votes
5answers
382 views

Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
4
votes
3answers
375 views

Creating a 3D List Line Plot From Discrete Points

Given the following Runge-Kutta ODE solver and the graphical output below, how do I get a 3D line plot instead of a 3D point plot? I see that there is no ListLinePlot3D function, so I thought it might ...
4
votes
3answers
267 views

DSolve not finding solution I expected

Try to solve the following ODE via DSolve $$ \left\{\begin{aligned} y'(x)+2 y(x) e^x-y(x)^2 &= e^{2 x}+e^x \\ y'(0) &=1 \end{aligned}\right. $$ The ...
4
votes
3answers
297 views

Plotting the direction field of a differential equation

I have to sketch the direction field for the following differential equation: $$\frac{dy}{dx}=\frac{-0.02 y +0.00002 xy}{0.08 x-0.001xy}$$ This is the code I used, which gives an incorrect plot: ...
4
votes
3answers
289 views

How could I get the value of y[t] at each specific interpolation point?

sol = NDSolve[{Derivative[2][y][t] + Sin[y[t]] == 0, Derivative[1][y][0] == 0, y[0] == 1}, y, {t, 0, 2}] the above-mentioned differential equations can be solved ...
4
votes
2answers
372 views

Finding a 3d curve from torsion and curvature with NDSolve

I'm trying to use the Frenet–Serret formulas to find the curve that matches the torsion and curvature I specify numerically with an InterpolatingFunction. The ...
4
votes
2answers
1k views

How do I plot a solution of a differential equation?

I am having trouble generating a plot for a solution to my differential equations. I always end up with just blank axes. ...
4
votes
2answers
2k views

Problem with the DSolve function

OK guys, here's the thing, Mathematica does not return a solution for this system of differential equations: ...
4
votes
2answers
262 views

Error entering equation in DSolve

I entered a command incorrectly as follows: DSolve[{y'[x]=y[x]},y[x],x] I am now experiencing: ...
4
votes
1answer
503 views

Solve inhomogeneous Poisson's equation, gives no result at all

I would like to solve the following two-dimensional inhomogeneous Poisson's equation in Mathematica including specific boundary conditions, and I know that an analytical solution exists, but ...
4
votes
2answers
5k 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 ...
4
votes
1answer
171 views

Using NDSolve to solve Equation of Motion in cylindrical coordinates

I have a set of coupled differential equations which represents the equation of motion of a particle in cylindrical coordinates with the following Hamiltonian: $$ H=\frac{1}{2m} \left( p_r^2 + ...
4
votes
1answer
105 views

NDSolve`ImplicitRungeKuttaGaussCoefficients doesn't work

I am using Mathematica 9.0 on Ubuntu. I tried the first example from this documentation page, but it returns unevaluated: ...
4
votes
3answers
1k views

Lyapunov Exponent

Does anyone know a (simple) Mathematica code for computing the Lyuponov Exponent for the Rossler System? Thank you Rossler System: ...
4
votes
3answers
515 views

Numerical solution of a differential equation with NIntegrate coefficients

I am trying to solve a linear ODE with a variable coefficient which is given in terms of an integral I can only do numerically. That is, I have an equation of the form $$ ...
4
votes
1answer
740 views

Evaluation of a Variable Coefficient PDE

I am trying to render the solution of the following partial differential equation: $$ u = u(x,y)~;\quad \frac1{x^{2/3}}\partial_xu + x^3\partial_yu + \partial_y^2u + \partial_x^3u = 0 $$ ...
4
votes
2answers
130 views

NDSolve fails to solve vector-valued function x'[t] == a . x[t] + u . b

I get no solution when I run the following command: ...
4
votes
1answer
183 views
4
votes
1answer
191 views

My mistake or error in NDSolve?

I try to solve the following equation $$y'=y-2ye^{-0.8y}, \quad y(0)=0.7.$$ By some aruments I expect to have a positive solution $y(t)\geq0$, for all $t>0$, however, NDSolve shows that starting ...
4
votes
1answer
388 views

NDSolve problem with matrix valued function

I got a strange problem when using NDSolve to solve a matrix value function σ[t] = {{σx[t], σxy[t]}, {σyx[t], σy[t]}} when I ...
4
votes
1answer
512 views

Can DSolve solve systems with unspecified function coefficients?

I am an economic research student with no previous experience with Mathematica, so please pardon me if my questions sounds really stupid. I am hoping to solve a system of nonlinear ODEs symbolically. ...
4
votes
1answer
886 views

Incorrect solution of diffusion equation with Neumann boundary conditions

I want to set up a PDE model, which takes a two-dimensional diffusion equation into account. The key problem is that I have some trouble in solving the two-dimensional diffusion equation numerically. ...
4
votes
1answer
691 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 ...
4
votes
1answer
75 views

Factoring a differential equation into an operator product

Following the fundamental theorem of algebra, I can (as stated here in Sec. 1.1.4) factor an $n$th-order linear ordinary differential equation $$ a_n \frac{d^n x}{dt^n} + a_{n-1} \frac{d^{n-1} ...
4
votes
1answer
146 views

Solving a nonlinear, second order d.e. in Mathematica

I am trying to solve the following differential equation $$ s''(x) = \frac{8}{9}s(x) -2s^2(x) + s^3(x), $$ with boundary conditions $s(-30) = 4/3 $ and $s(30)=0$, in Mathematica by using the following ...
4
votes
1answer
95 views

How to use WhenEvent with a vector ODE in NDSolve

I have an ODE system I'd like to specify as a vector equation in NDSolve. I'm not clear on how to use WhenEvent for a system ...
4
votes
2answers
110 views

Non-convergance of the solution of the 1+1 partial differential equation

I am stacked with a partial differential equation as follows: This is the $\LaTeX$ expression for the equation $$ \frac{\partial y}{\partial t}=\frac{\partial^2 y(x,t)}{\partial x^2} ...