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# Questions tagged [differential-equations]

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

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### How to plot population growth model?

How would I draw the graph of a function $\frac{dy}{dt}=(Ry^2/T)-Ry$ in Mathematica? I have tried a few times but the constants are confusing me.
934 views

### The only usage for the option InterpolationOrder in NDSolve is to be set to All?

We know that changing the option InterpolationOrder in ListLinePlotListPlot3D、...
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### Problem with NDsolve for a system of equations

I want to solve a system of differential equations which is not very complicated, but I cannot handle the problem with mathematica!! Please have a look at the problem and result and help me with your ...
616 views

### Numerically solving PDE with high precision

I want to numerically solve the PDE $\partial_t u(t,x)=c\partial_x u(t,x)+(mx-l)u(t,x)$ with some initial and boundary conditions and given parameters $c$, $m$ and $l$. Consider the code ...
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843 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?
167 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? ...
715 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 ...
261 views

### EventLocator with LSODA?

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

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

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

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

By running the following code: ...
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### 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 <...
5k 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 ...
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 ...
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### 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 ...
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### 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: ...
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### 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 ...
341 views

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

Below first case which gives particular solutions of an OED correctly: ...
8k 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, ...
2k views

### Manipulate a Differential Equation result

I want to Manipulate the result of Differential Equation like : ...
448 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 ...
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### 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 ...
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 ...
2k 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: ...
904 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 ...
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### 3- dimensional plot of 2-dimensional systems of differential equations

Let's take this first example of a 2D output: ...
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### 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 ...
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### 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}} )}, X[t], t] It is a system of 2 ODEs coupled by the matrix A, ...
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### 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. ...
710 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 ...