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

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123 views

Solve differential equation with undetermined constants making the assumption that the constants are positive

I want to solve: eqn = D[f[w], {w,2}] + (3/2 c^2 k Exp[c w] - 9/4 c^2 k^2 Exp[2 c w]) f[w] + m^2 f[w] sol = DSolve[eqn == 0, f[w], w] with the assumption ...
0
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0answers
212 views

Defining extra boundary conditions for NDSolve?

I have a second order reaction / diffusion type ODE of the form $\frac{D_{o}}{r^2} \frac{d}{dr}\left(r^2 \frac{dC}{dr} \right) - \frac{aC}{C+k} = 0$ where $a, k$ and $D_{o}$ are constants and $C$ is ...
-1
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1answer
183 views

Linking two differential equations

The solution and plot of the Differential equation is $\frac{d^2S(r)}{dr^2}+\frac{1}{r}\frac{dS(r)}{dr}-S(r)+3S^3(r)=0$ ...
-1
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1answer
429 views

plotting the solutions of system of differential equations [duplicate]

The following code include the system of differential equations: ...
1
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1answer
188 views

Dsolve too slow — is there anyway around?

I am trying to solve: ...
3
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1answer
252 views

Modelling the effect of a structure on a “tsunami” (hyperbolic wave equation)

So, the hyperbolic wave equation can be quite easily solved in Mathematica like this: ...
2
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2answers
201 views

How to pick out specific parts of the solution of a differential equation efficiently?

I'm trying to solve a set of differential equations (in parallel) and then select specific parts of the solution. What I have at the moment (see below-I've simplified the differential equations, in ...
2
votes
1answer
72 views

Incorrect information displayed when slider is moved (intermittent)

All, the following code graphs 10 different solutions for a first order ODE and allows the user to modify certain equation parameters to see how the graph is affected: ...
4
votes
2answers
510 views

DSOLVE for tenth order boundary value problem

I am currently using Mathematica 9 to find solutions for higher order ordinary differential equations. The following was my input for a tenth order boundary value problem (BVP): ...
2
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2answers
516 views

How to generate 2D FEM mesh in Mathematica?

To generate 3D mesh TetGen can be easily used. Are there similar functions (or a way to use TetGen) to generate 2d mesh? I know that such functionality can be easily implemented but I would like to ...
7
votes
2answers
422 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, ...
0
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0answers
315 views

Plot basins of attraction using separatrices for particular pendulum

How can I plot the stable and unstable separatrices to make a graphic of the basins of attraction of this differential equation? ...
2
votes
1answer
307 views

Use output of NDSolve as an integration limit of NIntegrate

I've been working on a ODE, for a function y[t], that, due to it's complexity, has to be solved numerically. I then need to use the results of NDSolve, which I ...
3
votes
1answer
287 views

Transform recursion for coefficients into differential equation for generating function

Assume, one is given a linear recursion with polynomial coefficients for a sequence $(a_i)_i$, such as a[i] == i a[i-1] I would like to convert this recursion ...
6
votes
1answer
522 views

Modelling a Rocket Launch using NDSolve

I'm trying to model a rocket launch with Mathematica but I've run into a little problem since I don't know how to turn the thrust off. I'm using Newton's Law of Universal Gravitation plus an added ...
4
votes
1answer
232 views

Create ParametricFunction object without ParametricNDSolve

Documentation of v9 states that ParametricFunction is generated by ParametricNDSolve and ...
0
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1answer
525 views

Bifurcation diagrams for system of equations

I am interested in constructing a bifurcation diagram for parameter a in the dynamical system given in the code below. I want to see how parameter changes affect the stability of the system. The ...
0
votes
1answer
410 views

Can graph interpolating function, but not use it. Any thoughts?

When solving a system of differential equations numerically, I get two interpolating functions. I can graph both of these, but when I try to evaluate either of the functions at a point, it just spits ...
0
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2answers
188 views

Interpolating a ParametricFunction

Original domain of my independent variable t is 0 to 10 nanometers, but in Mathematica (as in most numerical software), it's good idea to solve differential ...
0
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0answers
274 views

NDSolve for a large system of coupled (complex valued) ODEs

The system under consideration here is a generalization of the one I discussed in this problem. Qualitatively, I am trying to solve a system of coupled nonlinear (up to order 4 in the dep variables) ...
4
votes
1answer
256 views

Changing a wave simulation

I want to adjust some code that I found on this Wolfram Demonstration: http://demonstrations.wolfram.com/WaterRipplesPassingThroughASlit/ Basically it shows a wave passing through a single slit. I ...
3
votes
2answers
379 views

Ploting a 3D vector field using Manipulate, VectorPlot3D and NDSolve

My aim is to plot a vector field of the following system with a few trajectories: $$r'(t)=i-l.r(t)-\text{ux}. r(t). x(t)-\text{uy}. r(t). y(t) \\ x'(t)=\text{ex}. \text{ux}. r(t). x(t)-\text{mx}. ...
4
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0answers
322 views

NDSolve: ProcessEquations and Reinitialize with Piecewise functions

I am having trouble with using NDSolve`Reinitialize when the system consists of a pieceise function. If we define the ODE system ...
1
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1answer
741 views

3D Phase Portrait with direction fields and sample solution curves [duplicate]

I have seen NDSolve and ParamtericPlot3D used for things like the Lorenz Attractor, but was wondering if there is a way to draw a 3D phase portrait for a system. Something akin to this: ...
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0answers
178 views

Having Mathematica solve or help solve a set of 8 equations

There is a set of DDE's that arise in leukemia dynamics and I'd like to find the equilibrium points of the system by setting all of the derivatives equal to zero. The system can be described in ...
1
vote
1answer
543 views

Problem in solving PDE

I have a problem in solving a type of PDE. The actual problem involves diffusion and adsorption in a trench, but here is a simpler example. I have two independent variables $t$ and $x$. There are two ...
2
votes
1answer
298 views

Limitations of ParametricNDSolve family w.r.t objective functions

Observation: I can see even for very simple modification in case of an scalar objective involving an definite integral in time ParametricNDSolve fails. Here is an ...
4
votes
1answer
185 views

How to demonstrate lack of stability with advection equation

I am trying to that using a coarse grid with an explicit method for, say, the advection equation leads to an unstable solution. The trouble is Mathematica avoids unstable solutions with good ...
3
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2answers
295 views

How do I find the best fit?

I am trying to solve following system of three differential equations ...
2
votes
1answer
374 views

Crank-Nicolson with NDSolve?

As far as I understand, the Crank-Nicolson method (a.k.a. trapezoidal method) can be expressed as a second order implicit Runge-Kutta method. It's Butcher tableau is: ...
0
votes
2answers
414 views

Manipulating differential equations

I would be very grateful if anyone could help with manipulating the solution to the system of differential equations below. I've tried just about everything I can think of all to no avail. The code ...
2
votes
0answers
163 views

Using WhenEvent for derivative of discontinuous function

I have a discontinuous function ($u(t)$, a square wave) and I would like WhenEvent to trigger when the signal goes high/low, i.e. when the value of $u(t)$ changes. ...
3
votes
1answer
235 views

Utterly confounding behaviour in Mathematica 9 DSolve

I've been baffled by a lot of the behaviours of Mathematica 9 — so much that I regret upgrading my copy of Mathematica 8 (I would downgrade but I'm currently on vacation). Here is an example: ...
1
vote
1answer
114 views

Incorporating a Manipulation in an Animation

I am having trouble incorporating a manipulation into my animation. I want to be able to maniuplate the 5 constants at the beginning. Am I going to need to combine all of the code into one string? ...
1
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1answer
183 views

Using new symbol in WhenEvent in NDSolve

This is an example in Mathematica's help document. ...
1
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1answer
172 views

How can I eliminate $x_1$ from my two ODEs?

How can I get Mathematica to eliminate $x_1$ in the equations in the first box to achieve the equation in the second box? My code: ...
2
votes
1answer
738 views

DSolve doesn't find a solution

I have this partial differential equation (G and M are constants): and a solution is: Mathematica doesn't find any solutions. My code for DSolve is: ...
7
votes
2answers
276 views

Adding a constant vector to a vector differential equation seems to break NDSolve. Why?

I'm trying to solve a differential equation that's phrased in terms of matrices and vectors. My minimum working example is this: ...
1
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1answer
175 views
1
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2answers
345 views

How to define a function based on the output of DSolve? [duplicate]

I would like to define a function based on the output of the following DSolve call: ...
-3
votes
1answer
196 views

NDSolve doesn't solve my system of ODEs

What is causing the error in this code? ...
0
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2answers
258 views

Autonomous equations' critical points and eigenvalues

I have three-dimensional autonomous equations and want to find their critical points and corresponding eigenvalues. They have 6 critical points each. x, ...
0
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0answers
175 views

How can I solve my non-linear ODE?

DSolve[{-x^2 + y[x]^2 - 2 x*y[x]*y'[x] + 2*x^2 *y'[x]^2 == a^2}, y[x], x] DSolve is returning the input statement unevaluated. ...
3
votes
1answer
261 views

How can I deal with a non-numerical value for a derivative at $t = 0$ when using NDSolve?

I want to solve two coupled equations with NDSolve, ...
17
votes
2answers
2k views

How to fit 3 data sets to a model of 4 differential equations?

I'm a biologist and a newbie in Mathematica. I want to fit three data sets to a model consisting of four differential equations and 10 parameters. I want to find the parameters best fitting to my ...
8
votes
1answer
398 views

Complex valued 2+1D nonlinear PDE using NDSolve

I am trying to follow the main ideas presented in this question, applying it to my own problem, which is a complex, time-dependent, nonlinear PDE: $$i \frac{\partial \psi}{\partial t} = \left[ ...
6
votes
1answer
245 views

solve ODE with divergencies

The solutions of the second order differential equation $$\frac{1}{\eta}\frac{d}{d\eta}\left(\eta \frac{df}{d\eta}\right)+\left(1-\frac{s^2}{\eta^2}\right)f-f^3=0$$ is shown in Fig. 5.2 below, for ...
2
votes
0answers
62 views

Are FEM methods integrated in NDSolve yet? [duplicate]

About a year ago there was a discussion on these forums as to whether FEM methods have already been integrated into NDSolve in Mathematica. The answer back then was ...
4
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0answers
800 views

Numerically solving system of partial differential equation

I am trying to solve a system of partial differential equation with boundary conditions. But I got an error message saying NDSolve::icfail: Unable to find initial ...
5
votes
1answer
157 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: ...