Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
4,243
questions
0
votes
1answer
19 views
Solving a nonlinear PDE
I'd like to know the stationary ($t\to\infty$) behavior of
$\partial_tu=-y\partial_{y}u + \partial_y^2u+x^2+yx\partial_{x}u-(1+\partial_xu)^2 $
with $u(0,x,y)=0$.
DSolve doesn't give anything
...
3
votes
1answer
50 views
How to get the frequency response with the unstable branches for a nonlinear driven system?
I'm working on a driven system and want to get the amplitude-frequency response curve with an unstable branch just like the following one
where the dashed lines correspond to the unstable branches ...
0
votes
0answers
21 views
Non-Numerical Error Solving ODE [on hold]
In using NDSolve, I return the error:
*'NDSolve:Encountered non-numerical value for a derivative at t == 0.'*
Though I believe I've set every non-numerical ...
1
vote
0answers
28 views
Setting custom boundary conditions in pdetoode
I am solving a mix of PDE and ODE for two functions c1(x,t) and c2(t). Several answer point to the use of the function pdetoode.
I would like to use that function, but set the my own boundary ...
1
vote
1answer
85 views
How to solve PDE with periodic and anti-periodic b.c.?
I need to solve the PDE for a complex function $A(x,t)=A_r(x,t)+iA_i(x,t)$
...
2
votes
0answers
38 views
Speed up NDSolve for an integro-differential equation
On the MMA.SE, there have been several user cases on how to solve integro-differential equations using NDSolve, see example 1, example 2, and example 3. Many people,...
1
vote
1answer
63 views
Does 2D time dependent Schrödinger equation example work?
I have entered the example: www.wolfram.com/mathematica/new-in-10/pdes-and-finite-elements/solve-a-wave-equation-in-2d.html
into 12.0, and gotten an error message in the uifWave assignment. It says,...
0
votes
1answer
34 views
Evaluation functions with lower and upper limit ODE?
How do I find the numerical value of y at 0 and also at 1. Here is my code. I appreciate any help.
...
0
votes
0answers
30 views
Implicit definition of a coordinate in differential equation [duplicate]
I would like to solve the following differential equation
$\frac{d^2 \psi(r_*)}{dr^2_*} + (\omega^2 - V(r)) \psi(r_*)=0$
and the boundary conditions are $\psi(\inf) = \psi(-inf) = 0$. The problem is ...
0
votes
0answers
94 views
How to integrate this expression one time? [duplicate]
How can I integrate this expression? I want to have the second derivative of V i.e. V''[r]. Note that, you can multiply it be ...
0
votes
1answer
143 views
How to solve this differential equation analytically?
How can I DSolve the following differential equation?
Is there an analytical answer to this equation?
...
0
votes
0answers
43 views
Problems with DAE solution: “Structural analysis indicates that 1 initial conditions are needed to fix the state of the system…”
I'm trying to solve the following problem:
...
6
votes
1answer
116 views
How to solve this 1st-order linear ODE system with a few discrete eigenvalues?
I am trying to solve the eigensystem of a 1st-order linear ODE system in the region $(-\infty,\infty)$ and with Dirichlet boundary condition at the infinities
$$
-i\partial_xu(x)+f^*(x)v(x)=\lambda u(...
1
vote
2answers
56 views
Cannot solve coupled stochastic differential equations and how to find correlation of solutions?
I am trying to solve the equations
$x'[t] = y[t]$,
$y'[t]+(w^2+4*\gamma^2)x[t]+\gamma*y[t])=B[t]$
with the initial conditions $x[0]=0,y[0]=v_0$
This is what I have tried.
...
0
votes
0answers
60 views
Why doesn't DSolve work here?
I am trying to run this code (where f1, f2 and a1 are positive constants):
...
-3
votes
0answers
30 views
How to solve Riccati transformation? [closed]
Question 1.
A method that sometimes softens a stiff equation is the Riccati transformation based upon the logarithmic derivative Alpha=y'/y.
a) Create a set of transformation rules which apply the ...
1
vote
0answers
89 views
NDSolve 2 functions 2 variables with intermediate calculation : (1 time-space eq) + (1 space eq)
I have a system of differential equation with this structure :
$$\left\{\begin{split}&\partial_t n(t,r) + \nabla. \big(n(t,r)v(t,r)\big)=0 \\ & f\Big(n(t,r),v(t,r),\partial_r n(t,r),\...
5
votes
1answer
98 views
Problem with using NDSolve on wave PDE on string
I am trying to verify my hand solution for wave PDE in 1D, on a string. The solution I get from NDSolve does not match the analytical solution.
This is a string, ...
1
vote
1answer
57 views
DSolve does not solve 2nd order linear PDE with variable coefficients
I find that DSolve can solve
DSolve[x*D[u[x, y], {x, 2}] - D[u[x, y], x, y] == 0, u, {x, y}]
or
...
1
vote
1answer
37 views
Solving a System of Differential Equations for Pendant Drop Application
So I'm trying to solve the system of differential equations describing a pendant drop. The system is as follows:
...
0
votes
0answers
30 views
Plotting 2D and 3D data for a nonlinear system in mathematica
I had to plot various nonlinear differential equations. But because of a large number of equations for large spans of time and other considerations, the program has become too heavy to be run on my ...
10
votes
0answers
155 views
Workaround for DSolve in V 12 when it gives undefined as solution to 1D heat PDE?
Reported to WRI CASE: 4278450
Comparing the following, all done from clean kernel
The strange thing is that V 12 can solve this same PDE without the assumptions
...
0
votes
1answer
69 views
How to solve a differential equation like this one? [closed]
Does anyone know how to solve this equation in Mathematica
dx/dt = f(x) + u
where
f(x) = -x, if x < 1 or x = 1
4
votes
2answers
96 views
WhenEvent&NDSolve: How to detect saddle point?
I'm considering a simple ode. With the help of WhenEvent and Discrete Variable it is possible to detect the sign of the ...
0
votes
0answers
54 views
Numerical solution of a PDE having boundary conditions
I am solving a PDE using Mathematica. and I would like to know how to implement the condition that the three-variable function u[t, x, z]
...
1
vote
4answers
126 views
How to fit polynomial curve using Mathematica for multiple inputs?
I am new to mathematica. I have 3 inputs and 1 output. I want to find the 'N' th degree of polynomial which would approimately fit my dataset. I tried FindFit but it does not solve my problem. I also ...
0
votes
0answers
46 views
DSolve Coupled Equations
I'm new to Mathematica, and I am trying to solve a system of coupled equations with complex conjugates using DSolve before trying NDSolve.
So far my code does not work, I was wondering if maybe you ...
0
votes
2answers
43 views
How to solve a complex equation
I am trying to solve a complex equation for 'z' in terms of 'f'. At the moment my Mathematica is stuck running...
Just wondering if anyone has any ideas, I know 0 < z < 40 if that helps.
<...
3
votes
2answers
63 views
Plotting the derivative of NDSolve divided by the solution
I'm trying to solve the Friedmann equation as is given by:
$$
H^{2}=\Big(\frac{\dot{a}}{a}\Big)^{2}=H_{0}^{2}\big(\Omega_{m,0}a^{-3}+\Omega_{r,0}a^{-4}+\Omega_{\Lambda,0}a^{2.3}+\Omega_{k}a^{-2}\big),...
0
votes
0answers
108 views
Finding eigenvalues of a differential operator
I am trying to get the eigenvalues of the following differential operator
$$L\psi(r) = -f \partial_r (f \partial_r \psi(r)) + V \psi(r)$$
which must satisfy (obviously)
$$L \psi(r) = \omega^2 \psi(...
0
votes
0answers
36 views
Some issues with DEingesystem
I would like to solve (get its eigenvalues/vectors) the Sturm-Liouville problem, for the following differential operator: $L =\partial_{r} \partial_{r} \psi(r)$. Also, I would like to impose the ...
1
vote
1answer
60 views
Piecewise with differential equations
I have the following differential system. The calibration I use is as follows
...
1
vote
0answers
63 views
How could I know the Method adopted in NDSolve?
In NDSolve, different methods may lead to different results. For my codes
...
5
votes
1answer
133 views
Runtime too long for NDSolveValue, FindRoot breaks down at sharp turns
I have two equations:
$$
\frac{2}{3}\thinspace\left(\frac{\varepsilon}{\Delta}\right)^{\frac{3}{2}}=\sum_{i=1,2} \sigma_i\lambda_{i}\left(1+\lambda_{i}^{2}\right)^{\frac{1}{4}}E\left(\frac{\pi}{2},k_{...
1
vote
0answers
55 views
How do I find the function that is perfectly between y = x^2 and y = x? [migrated]
At first, I thought it was as simple as taking both functions adding them together then dividing by two, but this is not the case for what I am looking for.
Here is a plot of the following:
...
2
votes
3answers
137 views
Problem with boundary condition 2D heat transfer
I want solve this 2D Heat transfer:
So at Mathematica:
...
1
vote
0answers
33 views
How should I enter systems of equations as index notation?
I'm trying to numerically solve a system of ODEs that I've worked out in index notation where it's not clear to me what the matrix representation of many terms would be, and writing each scalar ...
1
vote
2answers
69 views
DSolve of second order DE results in InverseFunction
As a result of evaluating
DSolve[a''[t] a[t] - (1 - C) a'[t]^2 + (Cc - C L/3) a[t]^2 + (C - 1) k/2 == 0, a[t], t]
I got an ...
4
votes
2answers
239 views
Find multiple solutions of a nonlinear ODE
I have a nonlinear ordinary differential equation with two parameters c and R in the form of:
...
3
votes
1answer
64 views
Piecewise function not evaluating in NDSolve
Perhaps it's something obvious, but why does this simple piecewise function (as well as other conditionals) not evaluate in NDSolve:
...
0
votes
2answers
76 views
Getting the coefficients of a series that solves a differential equations
I have an example from Stewart's Calculus where the equation $y'' + y = 0$ is solved using power series. The equation
...
0
votes
1answer
70 views
Getting errors from ParametricNDSolveValue
I am a newcomer to Mathematica (use ver 9.0).
I just want to fit the experimental data to a system of odes' by using NonlinearModelFit. The data, contains time in the first column and product ...
0
votes
0answers
18 views
Parametrized vector function in PDE with DSolve/NDSolve
I'm trying to solve a PDE for a parameterized function $\vec x(s, t)$ where $t \in [0, T]$ and $s \in [0, T/h]$. This PDE reads as:
$\frac{\partial \vec x}{\partial t} = \vec u (s, t)$,
$ \vec x (s,...
0
votes
0answers
81 views
Problem with fitting
So I have a very simple question related to a simple topic, but also directly related to a fitting problem.
I see that my question is related to this question but I don't manage to make the bridge ...
6
votes
2answers
162 views
Ndsolve problem with Sign (friction)
In a very simple model I consider the motion of a body with frictional force.
...
1
vote
2answers
86 views
Problem with using NDSolve to solve coupled differential equations [closed]
I am having a problem with the following code:
...
1
vote
0answers
67 views
How to impose a “boundary” condition inside a computing domain?
I need to set a "boundary" condition not at the boundaries of the computing domain but inside the domain during solving an ODE with FDM. The problem is a boundary value problem, which has been ...
1
vote
2answers
108 views
Warnings using NDSolve on wave PDE. “Using maximum number of grid points” , “Warning: scaled local spatial error estimate”
Version 12 on windows 10.
I can't figure what should be changed in this call to NDSolve to make it happy.
This PDE is solved by ...
1
vote
0answers
65 views
NBodySimulation
My question is about new NBodySimulation package in version 12.
I figured out how to customize the basic functions "PairwisePotential", "PairwiseForce","ExternalPotetial"...
The next unresolved issue ...
2
votes
1answer
55 views
Problem finding separatrices for ODE system
I have a system of two ODEs for which I would like to plot the separatrices. I tried the very neat method given here by Michael E2. Unfortunately, that code doesn't work for my system since the ...
