Tagged Questions

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

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3
votes
1answer
387 views

Solving the Sine Gordon PDE in mathematica

how can i solve this equation in mathematica? this is sine-gordon eq. but the boundary condition can not recognized by mathematica . thank you for you attention. ...
3
votes
1answer
198 views

Construct DifferentialMatrices and Kernel for LevinRule for this integral and ODE set

I've made a lot of progress on my problem the last few days thanks to all the help I've received on here. I think I'm upto the final step of greatly improving the performance of NIntegrate[..] on my ...
2
votes
2answers
658 views

No result from DSolve

I don't get any answer when I evaluate the following expression: ...
2
votes
1answer
348 views

Vector Analysis: Why are the Grad, Laplacian and Div being evaluated to zero

For the non linear partial differential equation below, why are the Gradient, Laplacian and Divergence being evaluated to zero despite using the VectorAnalysis ...
3
votes
1answer
1k 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 ...
14
votes
3answers
538 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 ...
1
vote
1answer
293 views

Why is NDSolve solving in term of two 1st order ODE slower than 2nd order?

As mentioned in the documentation for NDSolve it's often convenient to reduce a 2nd order ODE to a system of first order equations. When I do this however I seem to see a significant speed reduction ...
2
votes
1answer
666 views

NDSolve runs out of memory

I need to solve a second order ODE numerically. The ODE depends on two parameters (a,b). Things work fine when 'a' is small, but for large 'a' the solutions are oscillating rapidly and Mathematica ...
10
votes
3answers
3k 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 ...
14
votes
1answer
1k 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 ...
8
votes
1answer
638 views

1D Euler Equations

Is it possible to accurately solve the 1D Euler equations in Mathematica using NDSolve? For example, let us consider the problem given here: http://www.csun.edu/~jb715473/examples/euler1d.htm Using ...
5
votes
1answer
499 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 ...
3
votes
1answer
1k 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 ...
6
votes
2answers
4k 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
1answer
436 views

Second Order Non Linear Differential Equation

I'm trying to solve the following differential equation numerically: ...
5
votes
0answers
233 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 ...
2
votes
1answer
191 views

tricky memoization

Let's say I have the NDSolve example for documentation involving splitting 2nd order into set of 1st order ODEs: ...
3
votes
1answer
395 views

Efficient way to perform elementary integration step with NDSolve internal method

I'm trying to tweak the NDSolve function to perform one elementary integration step (using some explicitly selected stepping algorithm via ...
2
votes
1answer
683 views

Solving a PDE containing DiracDelta

I want to get the answer from a PDE: $$\begin{align*} \frac{\partial \rho(r,t)}{\partial t}&=Dr^{-2}\frac{\partial}{\partial r}r^2h(r)e^{-U(r)}\frac{\partial}{\partial ...
0
votes
1answer
449 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?
2
votes
1answer
133 views

Using MaxStepFraction as ticks on plot

Is there any way I could use the MaxStepFraction (or grid size) as used in NDSolve in the example below as ticks on the 3d Plot? ...
1
vote
2answers
382 views

Replacing variable in an equation with an Interpolating function polynomial and plotting residual

I was trying to plot the residual for the solution of my PDE. However, I was unsure about a couple of things. I imported the data and created an Interpolation polynomial with ...
2
votes
0answers
182 views

EventLocator with LSODA?

Is the EventLocator option not compatible with LSODA on NDSolve. Below is what I tried to do ...
4
votes
3answers
317 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 ...
2
votes
4answers
278 views
14
votes
4answers
505 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 ...
9
votes
2answers
2k 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 ...
2
votes
2answers
888 views

export data points from differential equation system?

I am solving a dynamical three equation system. Besides plotting the individual effects for each of the state variables in an array and in a tridimensional graph, I would like to export the data ...
1
vote
1answer
859 views

Problem while solving system of two second order non linear coupled differential equations using NDSolve function

I am a completely new to Mathematica, and I am sorry if this question is dumb. I have to solve a system of two second order non linear coupled differential equations (that I got from the Lagrangian ...
3
votes
3answers
2k 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: ...
3
votes
2answers
500 views

How to avoid this kind of numerical error caused by extreme parameters when using NDSolve?

Here I use a one-dimensional heat conduction equation as the example. I found that when the thermal diffusion coefficient is small enough, Mathematica will give a result against the second law of ...
1
vote
1answer
200 views

Particular solutions of a Differential Equation not evaluated in a given case

Below first case which gives particular solutions of an OED correctly: ...
4
votes
2answers
2k views

How to handle NDSolve::ndsz problem (singularity problem)

I have 2 second order differential equations (non-linear). The physics behind them is correct. I verified the equations many times. It is a solid pendulum with a mass-spring at the end of it. Now, ...
2
votes
2answers
723 views

Manipulate a Differential Equation result

I want to Manipulate the result of Differential Equation like : ...
8
votes
2answers
290 views

Differentiating an unknown solution to a PDE

Sorry if this question is too basic -- I'm not very familiar with Mathematica. I am interested in a way to systematically address the following sort of problem: Suppose that $u=u(x,y)$ is a function ...
2
votes
2answers
759 views

Interpreting the interpolating function and saving data to plot with external program

So far I have been solving non-linear pdes with NDSolve and then plotting the result with the in-built Plot3D and ...
7
votes
0answers
2k 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|) ...
0
votes
0answers
49 views

integro differential equation [duplicate]

Possible Duplicate: Integro-differential equation I have to solve an Integro-differential equation with Mathematica or Matlab, in the following form: ...
6
votes
4answers
2k 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 ...
11
votes
1answer
688 views

I failed to solve a set of one-dimension fluid mechanics PDEs with NDSolve

The fluid here has been assumed as single component perfect gas i.e. it obeys the equation $p=ρ R T$, the thermal conductivity is assumed as a constant, so the equation set is: ...
4
votes
1answer
386 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 ...
6
votes
2answers
735 views
2
votes
2answers
1k views

Animation of Differential Equations from NDSolve with ParametricPlot3D and Evaluate

I have a system of differential equations (referred to as "s") and use NDSolve to obtain the solution. I substitute the interpolated functions for the original ...
6
votes
1answer
629 views

vectorial ODE in mathematica with matrix exponentials

I want to solve the following equation in mathematica : DSolve[{X'[t] == A.X[t], X[0] == ( {{0},{0}} )}, X[t], t] It is a system of 2 ODEs coupled by the matrix A, ...
4
votes
1answer
553 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. ...
3
votes
1answer
275 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 ...
0
votes
1answer
696 views

Fourier series of interpolating function result of NDSolve

I am having a tough time formulating the right question but here goes. I know that solving the pde as in here gives me an interpolating function. I understand that the interpolating function object ...
3
votes
2answers
390 views

How to set the initial condition? (to make IC and BC consistent)

I want to find the initial condition which fits mixed boundary condition of Phi[r, Theta, t]. The original initial condition in text is Phi[r, Theta, 0] == 1 . ...
1
vote
1answer
432 views

I ran into an error when I was trying to solve a PDE with a piecewise initial condition by NDSolve

This is a very simple one-dimensional heat-conduct equation, the only special part of it is the piecewise initial condition: ...
12
votes
4answers
9k views

How can I plot the direction field for a differential equation?

I'd like to plot the graph of the direction field for a differential equation, to get a feel for it. I'm a novice, right now, when it comes to plotting in Mathematica, so I'm hoping that someone can ...