Questions tagged [differential-equations]

Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

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1answer
64 views

System of nonlinear differential equations

I used the following commands: ...
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2answers
80 views

Differential equation system, Jacobian matrix, characteristic equation

We assume the differential equation system: $X'=σ(Y-X),Y'=X(ρ-Z)-Y,Z'=XY-βZ$. I can calculate the equilibrium points as: ...
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1answer
39 views

Plot global maximum point and differential equation

I have two questions: (1) I found the global maximum point of the following function ...
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1answer
203 views

Transient Heatflow in a Wheel Disc Brake

I try to model the Convection–diffusion equation for a rotating 3D annulus(small thickness): The temperature u[t,x,y,z] is described in cartesian coordinates. ...
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1answer
203 views

Simplifying solution to a third-order Boundary Value problem

I have been trying to solve a physical problem during which I reach the following third-order, Linear O.D.E. The solution I get using this expression is really messy. Is there any way to simplify it ...
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0answers
41 views

Difficulty Resolving the Meaning of K[1] and K[2] terms in DSolve Output

I am trying to analytically solve the following differential equation $2\dot a[t] \delta \dot a[t] = 8\pi G a[t]\big(6m^{2}(-3 + a[t]^{2}) \delta a[t] + a[t] \delta \rho[t] + 2\delta a[t] (\delta \...
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0answers
49 views

Improving NDSolve robustness (not blowing up)

I am trying to solve a heat conduction equation in Mathematica 9. While I can get NDSolve to work in some conditions it appears to arbitrarily fail if parameters are modified even slightly. Eventually ...
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0answers
40 views

Solving SDE system in Ito form

Can mathematica solve a linear SDE system in Ito form, for example $$ \begin{equation} \begin{bmatrix} dx_1 \\ dx_2 \\ dx_3 \\ dx_4 \end{bmatrix} = \begin{bmatrix} x_1 & ix_2 &...
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1answer
59 views

NDSolve not solving my equations

I'm trying to evaluate a fairly simple equation but the code I've written simply prints the equation as output. Originally there was a typo in the summation code but that seems to be fixed, anyone ...
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1answer
44 views

Trouble in the second order ordinary differential equations with second oder coupled iterm

I ran into a system of ordinary differential equations of second order and was puzzled by it for a few days. It was originally easy to solve, but because the coupling term is second order, it cannot ...
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1answer
142 views

How to write ODE for matrices?

This problem must have been encountered by many people but I could not find a neat solution googling. Many problems in mathematical physics can be written as a matrix ordinary differential equation (...
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1answer
61 views

Getting a stable solution for a simple first-order PDE

I have what is in my estimation a pretty simple PDE. It's the Liouville equation for the density of points in phase space with a hyperbolic secant potential. But when I try to solve it with NDSolve, I ...
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1answer
155 views

Solving partial integro-differential equation

I want to solve a partial integro-differential equation of this form: using NDSolve, something like ...
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3answers
239 views

Heat Flow in a Pipe

I try to model the transient heat flow in a pipe, assuming that the temperature in radial direction doesn't change: temperature ...
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0answers
71 views

DSolve struggles with simple differential equation?

Consider the set of differential equations equations = { f[x, y] + (x - y) D[f[x, y], y] == 0, D[f[x, y], x] == -D[f[x, y], y] } If we ...
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1answer
162 views

Inverse Laplace transform of this complicated function

I have been solving a coupled PDE system analytically and I need to find the inverse Laplace transform of $(1)$ and get $T(x,y)$. $s$ is the Laplace domain variable and $\alpha, \beta, \gamma, T_{fi}, ...
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2answers
190 views

Electrostatics: Finite Elements

I'm messing around with FEM in mathematica and am having trouble solving a very simple problem of the electric field around a unifromly charged sphere. Here is my workflow. ...
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1answer
92 views

Finding a functional form, solving a differential equation

I am giving my actual problem, but I would also like to understand how to solve such problems in general. I am neither a mathematician nor do I know a lot about Mathematica. I am looking for a ...
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1answer
115 views

Modeling a Partial Differential Equation

I'm in the midst of solving the given problem Given the setup I tried writing up the following: ...
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0answers
28 views

Relating `DSolve` solution to initial data for a PDE

The Liouville equation for a free particle is the PDE $$\frac{p P^{(1,0,0)}(x,p,t)}{m}+P^{(0,0,1)}(x,p,t)=0$$ For which Mathematica gives the solution in terms of the arbitrary function $$P(x,p,t)\...
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0answers
54 views

Swarming on Riemannian Manifolds

I am working on a swarm project on robot operating system, the control structure of the project is on page 32. Technical implementation is also available on page 32. I have successfully run it. This ...
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1answer
88 views

NIntegrate over regions, FiniteElement options

I am using NIntegrate to integrate a 3-dimensional region. When I don't set any integration options, I get a warning The global error of the strategy GlobalAdaptive has increased more than 2000 ...
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0answers
45 views

How to get the NDSolve to seek only a real solution?

I use NDSolve to solve system of 2 ODE of 1st order: ...
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0answers
80 views

Solving time dependent boundary conditions heat PDE

I am attempting to solve the heat equation $\frac{\partial T}{\partial t}=\nabla^2T$, where $T=T(x,y,z,t)$, subject to the following boundary conditions: $\frac{\partial T}{\partial x}|_{x=10}=\frac{\...
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66 views

Could you help me convert my PDE into a boundary value problem?

This is my code. It works as an initial value problem, but I want to solve it as a boundary value problem. ...
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1answer
50 views

NDSolve::deqn: Equation or list of equations expected instead of eqns in the first argument eqns

I am new to Mathematica, actually, I am working on a project based on Swarm Intelligence. I am trying to run a simulation of sphere formation of 10 robots, but there is a problem in equations. Here is ...
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0answers
31 views

Solving PDE with boundary condition (laplace equation)

I am wondering if Mathematica can solve the below PDE. Could somebody please help me? ...
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2answers
140 views

1DPoisson equation with Dirac delta

I was writing my own FEM method to solve the Poisson equation \begin{align} -u'' &= \exp(-c(x-1/2)^2)\\ u(0) &= u(1) = 0 \end{align} where c=100. and I'm reading from the book of Mats G. ...
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1answer
83 views

Using the results from NDSolve in another equation

I want to use the results sol returned from NDSolve (values of f at different ...
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1answer
92 views

Using GreenFunction in 2D free space for Laplacian

V 12. on windows. I have a question about using Mathematica's GreenFunction to verify known result for Green function for Laplacian in 2D. (I also have question ...
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1answer
78 views

More elegant/efficient numerical WKB implementation for 1D Schrödinger Equation

I'm trying to figure out a better way to implement numerical WKB quantization of a spectrum. WKB quantization is the condition that $$\oint_{E}p \, \mathrm{d}q = \pi \hbar (n+1/2)$$ So the idea to ...
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1answer
63 views

Allow Mathematica to solve the differential equations with larger than 16 digits parameters

Consider the system of differential equations ...
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0answers
74 views

Defining second derivative boundary condition using DEigensystem

I tried to solve a fourth-order eigenvalue problem with boundary conditions on high order derivative. For example, the following equation, $$\frac{\partial d}{\partial t}+\frac{\partial^4 d}{\...
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0answers
55 views

DSolve huge output

I get the correct answer for this differential equation ...
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0answers
28 views

Using assumptions in DSolve

I want to solve the following differential equation DSolve[u'[\[Xi]] == a u[\[Xi]]^(2 - m) + b u[\[Xi]] + c u[\[Xi]]^m, u[\[Xi]], \[Xi]] with the assumpetion ...
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2answers
147 views

Error trying to solve a 2D elasticity problem using FEM package

I have the following equations $$\frac{\partial{N_x}}{\partial{x}}+\frac{\partial{N_{xy}}}{\partial{y}}=0$$ $$\frac{\partial{N_y}}{\partial{y}}+\frac{\partial{N_{xy}}}{\partial{x}}=0$$ where \begin{...
5
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1answer
92 views

Eigenvalues and numerical eigenfunctions for similar differential operators

I am looking to numerically approximate the eigenvalues and eigenfunctions for a differential operator I am working with, assuming $\pi$ periodic boundary conditions. Namely, I define the function $...
4
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1answer
166 views

Poor convergence for first order PDE using FEM (Laplace's equation in a disk)

Consider Laplace's eqn in the unit disk, r^2 D[u[r, t], {r, 2}] + r D[u[r, t], {r, 1}] + D[u[r, t], {t, 2}] == 0. The general analytic solution is easy to work out,...
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0answers
50 views

Help with DSolve using exact Mathematica System

In an attempt to error-trap a 3-D DSolve solution, resorted to an eccentric circle flat model (analog to non-geodesic circles on a sphere), for which the following is an abridged code : ...
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0answers
154 views

Solving for a minimum action path in mathematica

I am interested in computing a quantity that is mathematically defined as follows, $$\phi(x_1,x_2) = \inf_{T>0} \inf_{\gamma \in C^{x_2}_{x_1 }(0,T)} \int_{0}^T L(\gamma, \dot{\gamma})\mathrm{d}t$$...
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1answer
49 views

How do I solve a large system of differential equations with indexed functions?

I strongly suspect that matrix methods are the right answer here, but I am having trouble visualizing how to set it up. Imagine a large number of coupled functions: ...
4
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0answers
38 views

NDSolve`ProcessEquations inside Manipulate

NDSolve and NDSolve`ProcessEquations can handle equations with vectors on each side like this one: ...
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0answers
119 views

Need help with ParametricNDSolveValue for ODE with two variables and Do-loop

I' m trying to solve a tricky 2-nd order ODE with ParametricNDSolveValue for boundary conditions (BCs) y = 0 at R and ...
1
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1answer
76 views

Strange results from NDSolve after using a smooth (Tanh) function to approximate a discontinuous (jump) event

I am solving a system of ODE which contains a discontinuous ode (the equation v[t]== ...in the following code and it means that my ...
1
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1answer
53 views

Export the list of value for the system of equation in the Loop using NDSolve

I want to solve a system of ODEs in sweeping a parameter $\omega$, and in that final conditions need to be carried for the initial condition for the next value of parameter $\omega$. Also, I want to ...
0
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1answer
44 views

Seting a function with NDSolve

I want to set a function sg which is a solution of the NDSolve based on a position x, time t ...
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0answers
101 views

Numerical integration of damped wave equation

I am trying to solve the equation $$ \frac{d^2u}{dt^2}-\frac{d^2}{dx^2}\left(c_s^2u+\nu\frac{du}{dt}\right)=0 $$ with initial conditions $$u(x, 0)=0$$ $$\frac{du}{dt}|_{t=0}=0$$ and boundary ...
3
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2answers
233 views

Solve a one dimensional heat transfer problem with NDSolve

The following problem is a 1-D heat transfer conduction problem: where, I am trying to solve with NDSolve like this way: ...

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