# Questions tagged [differential-equations]

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

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### Finding parameters for first positive root of solution to differential equation to be equal to a desired value

I have a differential equation with parameters. The objective is to vary the parameters such that the first positive root of the solution is equal to a desired value ...
1answer
2k views

### Decoupling system of differential equations

Here I have one task and it is preparation for small exam. I solved it by hand for first case 1), but I need to check it in $Mathematica$ and to try to implement it for both cases 1) and 2) ...
1answer
1k views

### DSolve output - understanding how to extract result

I'm a little confused with how to use the output from DSolve. The following works ...
1answer
1k views

### NDSolve Differential Equation Error

I am trying to solve the following differential equation- ...
1answer
550 views

### Solving the wave PDE using the Fourier method

I am trying to solve the wave PDE using the Fourier method and I need to animate the plots of the partial sum of order 45 -- U45(x,t) with initial conditions U45(x,t0), {t0, 0, 12, .2}. I am ...
1answer
814 views

### Optimizing the fitting of Ordinary Differential Equation(NDsolve) involving interpolation functions

I am a newbie to this forum. I am trying to use NDsolve to solve some ODEs involving the interpolation function. Then, I will compare the fitted curve and data to determine the ODE coefficients. ...
0answers
149 views

### Symbolic solution to ODE, pure InverseFunction not evaluated

I'm new to Mathematica and I don't understand why in the solution of the following ODE, the #1 in the pure function is not immediately replaced by the corresponding ...
1answer
2k views

### Lorenz map for the Rössler system [duplicate]

Possible Duplicate: How to find all the local minima/maxima in a range I have the solution of the following non-linear system: ...
1answer
742 views

### NDSolve for PDE with discontinuous initial/terminal condition

I have an issue with NDSolve for the case of a PDE with discontinuous initial/terminal condition. Consider the PDE solution ...
1answer
1k 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 ...
2answers
2k views

1answer
776 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. ...
4answers
8k 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 ...
1answer
542 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 ...
1answer
4k 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 ...
1answer
341 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 ...
1answer
928 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 ...
4answers
299 views

### How can I get the value of a at “t=2.4985352432136567” in the following expression?

By running the following code: ...
2answers
2k 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 ...
1answer
2k 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 ...
1answer
2k 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 ...
1answer
618 views

### Second Order Non Linear Differential Equation

I'm trying to solve the following differential equation numerically: ...
1answer
831 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: ...
1answer
275 views

### tricky memoization

Let's say I have the NDSolve example for documentation involving splitting 2nd order into set of 1st order ODEs: ...
1answer
2k 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 ...
1answer
166 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? ...
1answer
836 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?
0answers
260 views

### EventLocator with LSODA?

Is the EventLocator option not compatible with LSODA on NDSolve. Below is what I tried to do ...
3answers
1k 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 ...
2answers
3k 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 ...