Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
3
votes
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 ...
3
votes
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 ...
0
votes
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?
2
votes
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?
...
0
votes
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 ...
1
vote
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 ...
1
vote
0answers
124 views
EventLocator with LSODA?
Is the EventLocator option not compatible with LSODA on NDSolve. Below is what I tried to do ...
4
votes
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 ...
3
votes
4answers
268 views
How can I get the value of a at “t=2.4985352432136567” in the following expression?
By running the following code:
...
12
votes
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 ...
1
vote
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:
$$
...
3
votes
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 ...
1
vote
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 ...
1
vote
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 ...
3
votes
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:
...
3
votes
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 ...
1
vote
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:
...
4
votes
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, ...
2
votes
2answers
308 views
Manipulate a Differential Equation result
I want to Manipulate the result of Differential Equation like :
...
8
votes
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 ...
2
votes
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 ...
7
votes
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|) ...
0
votes
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:
...
5
votes
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 ...
9
votes
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:
...
5
votes
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 ...
5
votes
2answers
411 views
3- dimensional plot of 2-dimensional systems of differential equations
Let's take this first example of a 2D output:
...
2
votes
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 ...
6
votes
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, ...
4
votes
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. ...
4
votes
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 ...
0
votes
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 ...
4
votes
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
. ...
2
votes
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:
...
5
votes
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 ...
25
votes
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 ...
-2
votes
1answer
117 views
2
votes
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 ...
5
votes
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
$\dot{x}=f(x), \quad
\dot{y}=g(x,y)$
...
1
vote
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 ...
1
vote
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 ...
7
votes
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, ...
0
votes
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 ...
1
vote
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 ...
9
votes
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 ...
4
votes
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:
...
2
votes
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 ...
1
vote
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 ...
2
votes
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:
...
3
votes
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:
...
