Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
5
votes
1answer
352 views
Is it possible to do vector calculus in Mathematica?
I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components ...
3
votes
2answers
98 views
How can I get WhenEvent to recognize criterion I specify?
Using NDSolve I want to solve a differential equation till a quantity which is a function of the dependent variables reaches a certain value. My functions and criteria are complicated, but I am able ...
-2
votes
1answer
148 views
Problem with solving a differential equation [closed]
I need to solve the following differential equation:
NDSolve[{R[r, t], R[r, 0] == r/1000}, R, {t, 0, 30}, {r, 1, 30}]
Where ...
0
votes
1answer
89 views
1
vote
2answers
131 views
Discard ODE singular solutions with Mathematica?
The solution for a homogeneous second order linear ODE is generally a constant times one function plus another constant times a different function. Sometimes one of the solution functions is ...
0
votes
1answer
114 views
Setting boundary values of a second order differential equation
Not sure what is wrong with the boundary conditions for this problem:
...
0
votes
1answer
110 views
Subtracting results of NDSolve
I have 2 variables as a results from the NDSolve[] which are ua and uw.
This is how I do it, ...
12
votes
3answers
226 views
How to splice together several instances of InterpolatingFunction?
I have a set of InterpolatingFunction returned by NDSolve which are valid over different (but overall continuous) domains. How ...
4
votes
1answer
317 views
How do I solve a PDE with a strange boundary condition?
How do I solve the PDE with boundary value like this
$$u(t,x,y)=0, \textrm{when } F(x,y)=0$$
using DSolve?
As a specific example, I want to solve heat equation
$$\frac{\partial u}{\partial ...
1
vote
1answer
100 views
Using NDSolve solution as initial condition for another NDSolve
I have solved a PDE numerically using NDSolve, and I now need to be able to use that solution as an initial condition for another ...
0
votes
0answers
83 views
Need conditions for DSolve
If I have differential equation of fourth order with four solutions $\alpha _1,\alpha _2,-\alpha _1,-\alpha _2 $ where we have appearing the solutions in the form $e^{\text{$i\alpha $}_1 ...
0
votes
1answer
105 views
How to understand and use DSolve solution
This equation is simple to DSolve in Mathematica, but I don't know how to use and understand solution.
...
3
votes
2answers
229 views
How do I plot a solution of a differential equation?
I am having trouble generating a plot for a solution to my differential equations. I always end up with just blank axes.
...
2
votes
1answer
86 views
How to transform equation
Is there any possible way to write this equation of 4th order as a system of two diff equations of second order with two new variables and to do that automatically? statespace command is transforming ...
5
votes
1answer
109 views
How can I deal with an NDSolve::ivone message regarding boundary values?
I have a question regarding the error message:
...
6
votes
0answers
224 views
Modeling neural excitation with a non-linear differential equation
I think I have a special problem and I am not sure how to search for an answer, so I thought I would try here.
I am working with the so called FitzHugh-Nagumo model which describes very simple ...
1
vote
1answer
96 views
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 ...
0
votes
0answers
62 views
Inverse problem of Eigenvalues in DSolve
For my graduation exam I must prepare system of equations to satisfy some specific conditions. I have solutions, output 2, but I need equations eq11 and eq22. So here is an example.
...
0
votes
1answer
123 views
DSolve output - understanding how to extract result
I'm a little confused with how to use the output from DSolve. The following works
...
0
votes
1answer
252 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) ...
8
votes
1answer
180 views
0
votes
0answers
146 views
Boundary Value Problem
I have to solve this boundary value problem:
$$\frac{\mathrm{d}e_{3x}}{\mathrm{d}l}=(M_0+F_{0z}x-F_{0x}z)e_{3z}$$
$$\frac{\mathrm{d}e_{3z}}{\mathrm{d}l}=-(M_0+F_{0z}x-F_{0x}z)e_{3x}$$
...
0
votes
1answer
161 views
Solving the wave PDE using the Fourier method
I am trying to solve the wave PDE using the Fourier method and I need to animate the plots of the partial sum of order 45 -- U45(x,t) with initial conditions U45(x,t0), {t0, 0, 12, .2}.
I am ...
3
votes
1answer
332 views
How can I solve this PDE with initial conditions?
I wish to solve the following second order partial differential equation
$$u_{tt}=c^2 u_{xx}$$
with the initial conditions
$$u(x,0)=e^x,\quad u_t(x,0)=\sin x$$
In Mathematica, I evaluated the ...
0
votes
0answers
136 views
Another NDSolve with NIntegrate factors [closed]
My functions are:
$$E_x[x,z,t] := \frac {\gamma E_0 (x -
v t) } {(\gamma^2 (x - v t)^2 + z^2)^{3/2}}$$
$$I_x[x,z,t] :=
\int_0^{\infty} {e^{-e w} \sin(s w) E_x[x, z, t - w]} dw$$
with the ...
0
votes
0answers
177 views
ParametricNDSolveValue or NDSolve + fitting
I have been trying to find the value for the parameter kestim that yields the best fit of a model to some data points. datac has ...
1
vote
1answer
184 views
Optimizing the fitting of Ordinary Differential Equation(NDsolve) involving interpolation functions
I am a newbie to this forum. I am trying to use NDsolve to solve some ODEs involving the interpolation function. Then, I will compare the fitted curve and data to determine the ODE coefficients.
...
0
votes
0answers
72 views
A good choice to find solutions of ODE
In order to rephrase the question.
I would ask you to take a look at the following problem:
I have this system of ODE:
$$
\begin{cases}
\dot{x}(t)= x(t)[r_1(t) -b_1(t)x(t- \tau(t)) - c_1(t)y^m(t)] ...
0
votes
0answers
112 views
Diffusion equation with concentration dependent diffusivity, NDSolve has problem at C0> 10^20
I am using NDSolve to solve the diffusion equation:
D[Cp[x, t], t] == D[Dc D[Cp[x, t], x], x]
where Dc is a function of ...
0
votes
1answer
105 views
Some Problem with WhenEvent!
Anyone knows what's the problem with the following code and how can I fix it? I am not sure that I wrote the WhenEvent section correctly.
By the way, I want to solve the equations and then plot y vs. ...
3
votes
3answers
454 views
Lyapunov Exponent
Does anyone know a (simple) Mathematica code for computing the Lyuponov Exponent for the Rossler System?
Thank you
Rossler System:
...
3
votes
0answers
69 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 ...
2
votes
1answer
215 views
How to correctly use DSolve when the force is an impulse (dirac delta) and initial conditions are not zero
DSolve (and NDSolve) return different and unexpected solution to
differential equation when the input is an impulse. This is ...
0
votes
0answers
125 views
Numerical solution of a system of ODEs
I have to solve set of coupled first order ODE's
$y_1=z$, $ y_2=\frac{dz}{dt} $;
$\frac{d^2y_1}{dt^2}=\frac{dy_2}{dt}=\frac{(p_s-p_f)}{p_s}g-\frac{9u}{2a^2p_s}y_2 $
Using the Euler method and the ...
1
vote
1answer
153 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
...
0
votes
0answers
124 views
Solving differential equation with composite function [closed]
I'm trying to numerically solve this kind of differential equation:
NDSolve[{x''[t] == f[x[t]], x[0] == 0, x'[0] == 1}, x, {t, 0, 1}]
where ...
3
votes
2answers
366 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:
...
1
vote
0answers
148 views
NDSolve error when solving a BVP
I'm trying to solve the following BVP with unknown parameters (p and phi) using NDSolve over the period {Pi, 2 Pi}:
...
5
votes
1answer
104 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
...
1
vote
2answers
224 views
NDSolve problems of convergence
I have a big function that I have to maximize, so I have to evaluate some equation with thousands of different values of the parameter.
But the FindMaximum returns me many errors.
I have traced the ...
0
votes
1answer
119 views
Problem with #1's in DSolve
I've entered the following functions into my notebook, but the solution to them contains #1's that I can't seem to make any sense of. The functions are:
...
0
votes
1answer
119 views
Solving a simple BVP
I'm new to mathematica and am interested in solving the following BVP:
$\epsilon \,y'' + 2 y' + y^3 = 0$, for $0 < x < 1$ and $y(0) = 0, y(1) = 1/2$.
I have no experience with coding, so ...
1
vote
2answers
277 views
Problem with boundary values for a partial differential equation
I have a PDE problem that I can't solve. and I wonder if you could help me with it.
I have a Terzaghi Consolidation equation (similar to the heat equation) that is written as follows:
...
6
votes
2answers
151 views
Catching only the first event in NDSolve EventLocator
I have a system of ODEs that I solve. During the integration process, there's an event that I want to catch, but I want to (a) continue the integration after the event and (b) catch only the first ...
-3
votes
1answer
378 views
How can Mathematica solve this set of differential equations? [closed]
I'm trying to solve this set of non linear differential equations, but apparently it won't solve. I really tried all the tweaks I could think of. Still no progress... So now I turn to you, can you ...
6
votes
1answer
210 views
NDSolve and WhenEvent Causing Excess Work
When I use the following system
model = {x'[t] == x[t] (1 - x[t]) - x[t] y[t], y'[t] == x[t] y[t] - y[t], x[0] == 0.5, y[0] == 0.5}
with the ...
3
votes
2answers
118 views
Evaluate an ODE for several values of a coefficient and draw all the solutions in one plot
I want to draw one plot showing all the solutions the following ODE with different values of N. How can i do it?
...
6
votes
0answers
69 views
Return partial result when MemoryConstrained aborts NDSolve
I use NDSolve to solve a large set (~400) of coupled ODEs. Sometimes, the memory (~4GB) gets filled up, and my computer becomes impossible to work with, because it ...
0
votes
1answer
332 views
How can I understand the result Mathematica returns from DSolve?
I have solved an ODE using DSolve, but I have a problem with understanding the solution.
In general the solution is in the form:
...
3
votes
1answer
245 views
Eliminating functions from system of PDE in Mathematica
Mathematica users,
Let's see an example of three PDEs:
How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
