Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
1
vote
1answer
216 views
How to calculate a gradient at x=0?
I am solving a second order differential equation for n[x]. I solved it with both DSolve and NDSolve. A plot of n as a function of x looks great. Than I want to calculate a gradient of n[x] at a ...
2
votes
2answers
172 views
Weird NDSolve behavior with Piecewise (MMA9)
NDSolve in Mathematica 9.0.0 (MacOS) is behaving strangely with a piecewise right hand side. The following code (a simplified version of my real problem):
...
1
vote
2answers
283 views
Running a Numerical Simulation on a System of Differential Equations with unique initial conditions
I have a system of differential equations as follows:
...
1
vote
1answer
88 views
1
vote
0answers
141 views
Differential equation [closed]
I need to solve the following equation
$$
\left(v\frac{\partial L}{\partial v}-L\right)^{2}=\left(\frac{\partial L}{\partial v}\right)^{2}c^{2}+\frac{1}{M^{2}}\left(\frac{\partial L}{\partial ...
12
votes
3answers
229 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 ...
1
vote
1answer
125 views
Solving a system consisting of an ODE and a non-differential equation
I would like to solve the following system of equations:
y'[t] == x[t]*y[t] - x[t];
10 == x[t]*y[t]/(x[t] + y[t]) + x[t]/(x[t] + y[t]^2)
Is there any way to ...
9
votes
1answer
639 views
Numerically solving an inhomogeneous partial differential equation
I'm trying to solve a cylindrical partial differential equation with boundary conditions. But I got an error message saying ...
2
votes
2answers
156 views
Solving and plotting ODEs while varying one of the initial conditions
How can I vary an initial condition in the numerical solution of a system of ODEs and then make a 3D plot of the solution space with that condition as one of the variables.
...
11
votes
1answer
412 views
2D Heat equation: inconsistent boundary and initial conditions
I'm attempting to use NDSolve on a 2D boundary value problem with initial conditions. Upon running my code, I get the following message:
"NDSolve::ibcinc: Warning: Boundary and initial conditions are ...
5
votes
2answers
173 views
Symmetry-finding packages
Where can I find the most up-to-date or whatever you consider to be the most useful symmetry-finding package for differential equations? I do not intend to restrict to, but would like to include ...
0
votes
1answer
72 views
Evaluating derivatives for use in solve
I need to evaluate the derivative of a function. My function looks like
approx[vector_, x_] := Sum[vector[[n]]*Basis[n - 1, x], {n, 1, Length[vector]}]
and I'm ...
2
votes
1answer
158 views
Intermediate variables in NDSolve
I'm interested in using NDSolve as an integrator for a system of differential equations that looks like the following:
...
2
votes
3answers
268 views
How to calculate partial derivative of an unknown function
How can I force Mathematica to calculate symbolically the partial derivative of a function u[x,y] with respect to a variable ...
1
vote
0answers
123 views
NDSolve equations contain solution from solving cubic equations
I'm having trouble using NDSolve to solve equations that were obtained from solving cubic equations.
In my problem, I first obtained 6 functions (ca1, ...
2
votes
1answer
106 views
NDSolve problem with matrix valued function
I got a strange problem when using NDSolve to solve a matrix value function
σ[t] = {{σx[t], σxy[t]}, {σyx[t], σy[t]}}
when I ...
5
votes
1answer
355 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 ...
1
vote
1answer
391 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
2answers
99 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
149 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 ...
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 ...
0
votes
1answer
90 views
6
votes
0answers
225 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 ...
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, ...
1
vote
2answers
134 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 ...
2
votes
1answer
218 views
Partial differential equation: unexpected result from changing boundary region size
I am trying to solve a PDE for heat diffusion, but I have a problem with the boundary region. When I change the boundary region size, the estimation of temperature increases even when no other ...
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 ...
3
votes
2answers
232 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.
...
0
votes
1answer
107 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.
...
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
111 views
How can I deal with an NDSolve::ivone message regarding boundary values?
I have a question regarding the error message:
...
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.
...
3
votes
1answer
253 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 ...
0
votes
1answer
255 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) ...
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
...
8
votes
1answer
184 views
0
votes
0answers
137 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$$
with the ...
0
votes
1answer
163 views
Solving the wave PDE using the Fourier method
I am trying to solve the wave PDE using the Fourier method and I need to animate the plots of the partial sum of order 45 -- U45(x,t) with initial conditions U45(x,t0), {t0, 0, 12, .2}.
I am ...
0
votes
0answers
148 views
Boundary Value Problem
I have to solve this boundary value problem:
$$\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}$$
...
3
votes
1answer
336 views
How can I solve this PDE with initial conditions?
I wish to solve the following second order partial differential equation
$$u_{tt}=c^2 u_{xx}$$
with the initial conditions
$$u(x,0)=e^x,\quad u_t(x,0)=\sin x$$
In Mathematica, I evaluated the ...
0
votes
0answers
177 views
ParametricNDSolveValue or NDSolve + fitting
I have been trying to find the value for the parameter kestim that yields the best fit of a model to some data points. datac has ...
1
vote
1answer
185 views
Optimizing the fitting of Ordinary Differential Equation(NDsolve) involving interpolation functions
I am a newbie to this forum. I am trying to use NDsolve to solve some ODEs involving the interpolation function. Then, I will compare the fitted curve and data to determine the ODE coefficients.
...
0
votes
0answers
72 views
A good choice to find solutions of ODE
In order to rephrase the question.
I would ask you to take a look at the following problem:
I have this system of ODE:
$$
\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
114 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
106 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
464 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
219 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 ...
