Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
0
votes
0answers
39 views
Issues solving system of differential equations [on hold]
d = NDSolve [{x''[t] == (x [t] + a[t])/(-2), a''[t] == -x''[t]/2, x[0] == 0, x'[0] == 1, a[0] == 0, a'[0] == 0}, {x, y}, {t, 20}]
Keeps returning the error
"To ...
1
vote
1answer
46 views
System of coupled differential equations
I am trying to solve the following system of equations, but I get as the output the command itself.
...
2
votes
2answers
48 views
Finding the amplitude of function solved using ParametricNDSolve
I have been trying to find the peaks of a function I have plotted using ParametricNDSolve. I have to find these peaks to calculate the amplitude of all the various waves in the observed output. By ...
1
vote
1answer
75 views
Conditional evaluation: black hole cross section
I'm trying to calculate the collision cross section of black holes, more precisely, I want the critical impact parameter $b_{\text{crit}}$ for a given initial velocity $v$ such that, at this speed, ...
3
votes
2answers
100 views
Heat equation with variable conductivity
Let us consider the (very simple) problem
$\qquad \partial_x[k(x)\,\partial_xu]=0,\quad x\in [0,1]$
$\qquad u(0)=0,\ u(1)=1,$ with $l\in(0,1)$
$\qquad k(x)=\left\{\begin{array}{l}k_1^{},x<l\\k_2^...
4
votes
1answer
95 views
Concerning the origin of four terms in DSolve's hyperbolic solution to an ODE
Typing
DSolve[{g''[y] - k^2/Gy g[y] == 0}, g[y], y]
where $k$ and $G_y$ are constants gives
$$\left\{\left\{g(y)\to C_1 \exp\left(\frac{k y}{\sqrt{G_y}}\right)+...
2
votes
0answers
47 views
Solving a PDE solved by the method of lines giving a warning about bad local spatial error estimate
I use the method of lines to solve the PDE
...
2
votes
1answer
66 views
Help in advection-dispersion equation using NDSolveValue
i have the advection-dispersion equation:
Dz = 0.0000738739; as = 2.21622*10^-6;
Dz*D[u[z, t], z, z] - as*D[u[z, t], z] == D[u[z, t], t]
The boundary and ...
1
vote
0answers
27 views
Analytic solution of a system of six ODEs [duplicate]
I have a system of six ODEs for six function. I want to get the analytic solution of the system. I have used DSolve, but it can not solve it.
The code is:
...
3
votes
2answers
83 views
How to solve these ODEs using NDSolve?
I have six odes and I cannot use DSolve. So I tried NDSolve. But it says there may be some errors.The code is such like this:
...
1
vote
1answer
39 views
Use ParametricNDSolveValue for system of equations
I'm trying to use ParametricNDSolveValue for a system of equations. I want to have it create a function that takes in a single input and outputs a list. Here is my code thus far.
...
0
votes
0answers
62 views
Need help solving ODE
Can I solve the given equation using Mathematica?
A = Log[a]; H = 1/a*D[a[t], t];
DSolve[{1/H*H'''[A] - 20*H == 0}, H[A], A]
I am facing difficulties to solve ...
0
votes
1answer
44 views
Solve differential equations with matrix exponential [closed]
I wanted to solve a differential equations by matrix exponential
...
0
votes
0answers
45 views
DSolve leads to an equation that is different from paper solution
I'm following the method in the two images in an attempt to obtain a value for $\beta$. I know that there's a mistake in (4.36) from here so I used Mathematica's solution to continue the solution. I ...
2
votes
2answers
58 views
Extra constant in solution of ODE using DSolve [on hold]
A paper that I have states that the solution of the ODE
$$-\frac{\left(\frac{\pi k}{a}\right)^2 Y(y)}{G_y}+\frac{Y''(y)}{G_x}+\frac{8 \theta }{\pi k}=0$$
is
$$Y=A\sinh\left(\frac{k\pi\mu}{a}y\right)+...
0
votes
1answer
66 views
Why does my SIR differential equation solver not work?
I'm trying to solve a system of SIR differential equations with Mathematica.
My code is:
...
3
votes
1answer
105 views
How to specify non-reflective boundary conditions when NDSolving two coupled first order PDEs?
Due to a lack of fruitful answers after 3 days, this question has been reformulated in a more direct way compared to its first version.
Consider the telegraph equation problem expressed as a system ...
0
votes
1answer
48 views
I am trying to solve these Chemotaxis Equations but I can't seem to make it work
I am trying to solve a a pair of coupled partial differential equations but it doesn't seem to work. I am getting the error 'Length of the derivative order is not u1[t,x]the same as the number of ...
-1
votes
0answers
62 views
Analytic solution for two coupled Partial Differential Equations using DSolve [closed]
I am looking for an analytic solution to the following two coupled equations for $v(x,t)$ and $u(x,t)$:
$$\frac{\partial v}{\partial x}=-m \frac{\partial u}{\partial t}$$
$$\frac{\partial u}{\partial ...
0
votes
0answers
63 views
Solve a system of coupled partial differential equations in 2D
I am new at Mathematica and I am trying to solve this system of coupled partial differential equations in 2D in cylindrical coordinates, where the model is axysimmetric, around the z axis.
$\frac{1}...
0
votes
0answers
53 views
Fourier analysis. How to present a numerical solution of a nonlinear differential equation in the amplitude-frequency spectrum? [migrated]
I have a system of nonlinear differential equations:
...
1
vote
1answer
68 views
Problem finding constants after using DSolve
I have to solve a relatively simple PDE:
$$\frac{\phi_{xx}(x,y)}{A}+\frac{\phi_{yy}(x,y)}{B}=-2 \theta$$
where $A$, $B$, and $\theta$ are constants. The code that I used was
...
2
votes
1answer
26 views
Trouble using ParametricNDSolve in Manipulate
I have troubles to understand how to use Manipulate and ParametricNDSolve to have modulable parameters inside my models. I ...
0
votes
2answers
50 views
Dealing with Infinite expression errors
I'm currently trying to generate a plot showing what happens to a damped oscillator when it's critically damped using the following code:
...
2
votes
1answer
45 views
Eliminating Discontinuities When Using Mod with NDSolve and Plot for Oscillators
I have found similar questions to mine, but dealing with piecewise and parametric plots instead and unfortunately the answers don't seem to extend to my case.
I have a solution from ...
0
votes
1answer
62 views
Solving Coupled system of differential equation with NDSolve
I am solving a system with coupled system of differential equation to obtain the time evolution of two vectors. The problem stated here is equivalent to solving Landau Lifschitz Gilbert equationLLG ...
2
votes
1answer
72 views
Having trouble using WhenEvent with NDSolve
First of all, this is my first time on this forum. Please be patient with me because if I make some mistakes in this post. I'm not used to doing this!
I'm trying to modify a parameter during ...
1
vote
2answers
98 views
1
vote
1answer
64 views
Solve Euler Lagrange equation of motion DSolve
I'm trying to find Euler Lagrange equation of motion.
then DSolve the equation for list of variable x1,x2,x3,x4
Here is my code:
...
-1
votes
1answer
141 views
Working with motion equations
I'm trying to solve some Lagrange differential equations of motion, where $L = T - U$. Also, how can I use the solution for each x1, x2, x3, ..., xn?
Here is my code:
...
1
vote
0answers
73 views
How can I improve and accelerate my 2 D algorithm?
I implemented the algorithm descussed here in the 1 D case (when $g$ is one variable function). Using a relaxation parameter the algorithm became very fast and converges in few iterations (n = 5, 6, , ...
-1
votes
1answer
80 views
Solving 3 nonlinear, transient, coupled PDEs [closed]
I'm trying to solve the fluid equations, continuity equations for mass, momentum, and energy, for a transient shockwave in 1D planar geometry. A piston is traveling at some velocity $u_p$ where $u_P$ $...
1
vote
0answers
50 views
Absorbing/Derivative Boundary Conditions
I am attempting to solve a differential equation, however I am having issues implementing boundary conditions that reduce the impact of reflections/instabilities.
I've had a look at similar ...
1
vote
0answers
44 views
Slight change in boundary contains giving unexpected results
I cannot find out where the difference comes from.
First pde, solBM30, has variable boundary condition which I evaluate at a certain point. The second pde, ...
3
votes
1answer
60 views
Hypergeometric differential equation with integer parameters?
Naively, the hypergeometric differential equation has two independent solutions as follows:
...
0
votes
0answers
69 views
Numerical Solution of giant Analytic DE
I have a little bit of a problem regarding numerical solutions.
I have a system of two entirely symbolic differential equations of two functions, F[r] and K[r]. One of them is fairly simple, but the ...
0
votes
1answer
44 views
Update initial conditions recursively/sequentially within ParallelTable using NDSolve
I am modelling 3D motion of particles inside a force-field using second-order coupled PDEs, which I solve from time t=t0 to t=t1 with initial conditions x0,y0,z0. I have a total number of "particles" ...
2
votes
1answer
37 views
Using Series with Refine or Assuming to restrict the power
I have a system of differential equations which contain a singular point. To avoid the singular point, I am expanding the coefficients and solutions in a power series around that point.
Due to the ...
3
votes
2answers
131 views
Bifurcation diagram of nonlinear system of ODE [duplicate]
Welcome to all, I try to apply most suggestion codes of a plot bifurcation diagram but I could not, I got an error. Is there anyone who can help me to understand how I can plot a bifurcation diagram ...
0
votes
0answers
49 views
solving inside for loop and sorting x which are less than 3 and greater than -3 from the list
I give a simple function code here...
Clear[a, x, t];
s = ParametricNDSolve[{x'[t] + a*x[t] == 0, x[0]==1}, x, {t, 0, 100}, {a}]
y = x[1] /. s
y[5] /. s
I ...
0
votes
1answer
36 views
Cannot solve ODE question with Initial Value [duplicate]
I'm using Mathematica to solve the ODE problem y'=xy, y(1)=2.
However, when I put my equation into Mathematica, it only appears 'True'.I tried it the webpage http://develop.open.wolframcloud.com/app/ ...
0
votes
1answer
80 views
Creating a numerical table of values from an interpolating function resulting from NDSolve
I am trying to carry out point "Implementing Map" on this paper Interstellar wormholes however I am using my own equations not those given (only the same method).
Part 1
I am trying to create a ...
1
vote
3answers
319 views
How to deal with a Dirac delta function numerically? [closed]
I need to solve some differential equations with a Dirac delta function. e.g. the source terms are like, $\delta(x)$ and $\partial_x \delta(x)$.
Could I just use the Gaussian type function? e.g.
$$...
0
votes
2answers
101 views
Transform expression into a certain standard form for an ODE
I'm using Mathmatica 11.1 on Windows.
Given an expression containing a differntial equation of the form
$\qquad A\, x'(z) = C\, x''(z) - B\, x(z)$
Or
...
2
votes
1answer
55 views
Using Manipulate to show the solution of an ODE by NDSolve and DSolve
I can't spot the error, can someone help me?
...
1
vote
1answer
115 views
NDSolve in NIntegrate function, numerical values as a symbolic variables
I'm trying to implement the following iterative scheme $g_{n+1}=g_n-\int_0^t\Phi(g_n) dt$, where $g_n$ is a source term in a PDE and $\Phi$ is the solution of an adjoit problem associated to the PDE ...
0
votes
1answer
46 views
Using ParametricNDSolve with n subscripted functions
I want to calculate trajectories of an n-pendulum. For the number n=1 it's just a pendulum, for n=2 a double pendulum , for n=3 a triple and so on.
The Solver has to solve n equations for the angle. ...
2
votes
2answers
56 views
3
votes
1answer
157 views
One term in non-linear equations prevents NDSolve to work
I am currently working on the stratification of the core of the planet Mercury, meaning the formation of a conductive layer at the top of the convective core, with a moving interface between both ...
0
votes
0answers
77 views
Numerical integration: gravitational force
What I would like to accomplish is to numerically integrate the following equation:
$\nabla^{2}\Phi(r)=\rho(r)$,
to get $\nabla\Phi(r)$.
$r$ is the radial distance from the origin.
Suppressing the $...
