# Tagged Questions

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

1answer
252 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 Method option). Such a possibility is crucial for me, since ...
1answer
408 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 ...
1answer
309 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?
1answer
120 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? ...
0answers
141 views

### Trying to plot a solution to a DE on Mathematica [closed]

I am trying to solve and plot a solution to an ODE, but Mathematica keeps returning other useless answers In[0] DSolve[y'[x] == 1 + y[x]^4, y[x], x] Out[0] DSolve[True,y(x),x] Can someone ...
2answers
204 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 ...
0answers
124 views

### EventLocator with LSODA?

Is the EventLocator option not compatible with LSODA on NDSolve. Below is what I tried to do ...
3answers
132 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 ...
4answers
268 views

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

By running the following code: ...
3answers
263 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 ...
1answer
389 views

### How to solve a differential equation of nonhomogeneous fourth order real variable complex function with Mathematica? [closed]

Recently, I was got in trouble in solving a fourth order differential equation with Mathematica. And it is written like:  ...
1answer
600 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 ...
2answers
223 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 ...
1answer
490 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 ...
3answers
704 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: ...
2answers
244 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 ...
1answer
107 views

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

Below first case which gives particular solutions of an OED correctly: ...
2answers
612 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, ...
2answers
308 views

### Manipulate a Differential Equation result

I want to Manipulate the result of Differential Equation like : ...
2answers
192 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 ...
2answers
300 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 ...
0answers
1k 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|) ...
0answers
41 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: ...
4answers
517 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
465 views

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

@DNA The fluid here has been assumed as single component perfect gas i.e. it obeys the equation P=ρRT, the thermal conductivity is assumed as a constant, so the equation is: ...
1answer
177 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 ...
2answers
411 views

### 3- dimensional plot of 2-dimensional systems of differential equations

Let's take this first example of a 2D output: ...
2answers
589 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
387 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, ...
1answer
237 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. ...
1answer
154 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 ...
1answer
311 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 ...
2answers
276 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 . ...
1answer
215 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: ...
4answers
1k 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 ...
2answers
1k views

### Efficient Langevin Equation Solver

This question is not about good algorithms for solving stochastic differential equations. It is about how to implement simple codes in Mathematica efficiently exploiting Mathematica's programming ...
1answer
117 views

### Problem with NMaximize output [closed]

This is what I'm trying to do: ...
1answer
327 views

### Function output from DSolve

I want to get a function as output form DSolve. For Example : sol = DSolve[{Q''[t] + 40 Q'[t] + 625 Q[t] == 100*Cos[10*t], Q[0] == 0, Q'[0] == 0}, Q[t], t] I ...
3answers
407 views

### How to use results of NDsolve[] for further solving of ODEs?

I have a system of ODEs with 10 eqns. I can solve the first 5 independently. How can I use those results to solve for the remaining 5? An easy example would be $\dot{x}=f(x), \quad \dot{y}=g(x,y)$ ...
1answer
149 views

### Problem with Eventlocator Method for NDSolve

I want to solve the ode and plot the solution v[x] for different values of parameter a where ...
1answer
259 views

### Solution of numerical vector equation

Suppose I have a vector equation: Y'[t]==rhs[Y[t]] and Y[0]==ConstantArray[0,n] where "rhs[Y[t]]" is a black box function ...
1answer
327 views

### Optimizing an energy functional in mathematica using variational calculus

I have an energy functional which I want to optimize using calculus of variation. It would be nice if someone could please post a working example using mathematica. The procedure is as follows, ...
0answers
243 views

### Unexpected result from contour plot - where is the color gradient?

When I plot a contour plot of my (in)famous code :P I get some unexpected results that I don't quite understand. My code (the one that has ...
1answer
110 views

### Backward compatibility issues while DumpSaving Interpolation polynomials

I have bkwrd compatibility issues when I save my NDSolve result (which is an interpolating polynomia) using DumpSave from Mathematica 8 on Windows 7 and then try ...
1answer
387 views

### How to tell mathematica not to resolve stiffness issues

Very often I solve partial differential equations that are nonlinear and could be up to 4th order. In these cases, it is usual for the solution determined by ...
2answers
767 views

### Problem with the DSolve function

OK guys, here's the thing, Mathematica does not return a solution for this system of differential equations: ...
1answer
204 views

### Laplacian or Grad of an InterpolatingFunction

For obtaining a Schlieren image from an equation for density, I need to calculate the first derivative of density and make a contour plot. The below code snippet calculates the first derivative w.r.t ...
0answers
324 views

### Effectively Dirac delta in numeric PDE - Mathematica or Matlab solution?

I am trying to solve a following Partial Differential Equation: u_t(x,y,t)= u_xx(x,y,t)+u_yy(x,y,t) + 7 u(x,x,t) which causes troubles due to the last term ...
2answers
286 views

### How to solve a Differential Equation with DSolve with Function Coefficient?

Suppose I have v[x_] = (1.453 Sech[x + 1])^2 + I Sech[x + 1] Tanh[x + 1] And I have to solve the equation: ...
2answers
450 views

### optimization problem with NDSolve

I want to minimize the function fcc. When fcc is calculated for a specified point the answer is correct: ...
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