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Questions tagged [differential-equations]

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

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26 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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18 views

NDSolve and equations of motion

I am trying to use NDsolve to solve a set of coupled second order ODEs. Here are the initial conditions: ...
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30 views

One dimensional wave equation [on hold]

The sermon about the one dimensional wave equation is, that all solutions have the following form (to simplify we include the velocity into time t'= c t): $$ u_{t t} - u_{x x} = 0 $$ $$u(x,t)= F(x+...
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1answer
53 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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25 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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49 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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36 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
39 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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25 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
113 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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41 views

Brusselator Model - solution and graph [on hold]

I am trying to solve the Brusselator differential system and plot the solutions but I have a problem with DSolve - it doesn't give any result after a couple of ...
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1answer
46 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
61 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
65 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
57 views

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

Consider the system of differential equations ...
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20 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, with a homogenous Direclet condition at the edges and a ...
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53 views

DSolve huge output

I get the correct answer for this differential equation ...
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0answers
24 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
114 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{...
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1answer
71 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 $...
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24 views

Biot_Savart law for bounded current systems [migrated]

I have a PDE I don't know how to solve, which is a result of a physics problem related to the Biot-Savart equation. The PDE in question is an equation for B: curl(B)=del(phi) where phi is a known ...
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48 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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104 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
47 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: ...
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36 views

NDSolve`ProcessEquations inside Manipulate

NDSolve and NDSolve`ProcessEquations can handle equations with vectors on each side like this one: ...
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112 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 ...
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49 views

Basic Question: How do you represent simple equations of motion in Mathematica? [closed]

I'm trying to set up a simple sandbox to understand motion. First I want to represent linear motion in Cartesian coordinates, then in polar. The first step is a set of equations that represent ...
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1answer
73 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 ...
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1answer
51 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 ...
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1answer
40 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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90 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 ...
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1answer
127 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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1answer
117 views

Works with NDSolve, not DSolve

EDIT1: ...
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3answers
102 views

Constraint of NDSolve with an integral of the solution

I'd like to use NDSolve and to make a constraint with an integral. For example, take the very simple : $$f'(x)=-f(x)/x_0 $$ the solution is $$f(x)=f_0 e^{-x/x_0} $$ And $f_0$ is given by : $$\int_0^...
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2answers
86 views

NIntegrate failed to converge and why?

i have put up and question about the NDSolve and have got the solution of the ODE,and also got the figure of t1-t ,however when ...
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3answers
147 views

NDSolve will try solving the system as differential-algebraic equations but it didn't get the solution

Please help me deal with this kind of question about ODEs. My codes are as follows ...
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1answer
38 views

Confusing behavior of LQR control that strongly depends on system output (with odes solved by NDSolve)

I am implementing a LQR control of a 3-floors structure. Firstly, I obtained a reasonable result with my first code (Code 1 as shown below). In this code, the ...
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1answer
48 views

Visualizing a system of differential equations [closed]

I have the following system of differential equations: x'[t] == x[t] - x[t] y[t] y'[t] == x[t] y[t] - y[t] I use this Wolfram Mathematica code: ...
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1answer
86 views

Bifurcation diagram

I have a differential equation y''[t] + 0.3*y'[t] - y[t] + (y[t])^3 == A*Cos[114.14*1.2*t] with y'[0] == 0, y''[0] == 0 t varies from 0 to 1500, A varies ...
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1answer
35 views

Singularity or stiff system in NDSolve

I have the following piece of code ...
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1answer
52 views

How to address an element of variable vector for coupled system of ODE while using NDSolve

I am using Mathematica from around 10 months. I want to solve numerically a system of equations with number of equations more than 35 to 40. System of equations is shown below for small number of ...
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1answer
53 views

Why does this stiff BVP return unevaluated but a similar IVP produce a solution?

In Solving a steady-state viscous Burger's equation with NDSolve, one question involves the following problem: ...
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62 views

Solve ODE system efficiently with mathematica

I've been trying to solve a system of ODE's with mathematica, which is a master equation of a hierarchically organized tissue model, where I want to quantify the number of cells at level 'k' with 'm' ...
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108 views

Nonlinear, second order system of ODEs not solved by Mathematica, solution however exists

I am currently working on solving a system of two coupled nonlinear second order ODEs. I have already shown by hand, that 2 real solutions, as polynomials of second order, exist but I want to use ...
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1answer
161 views

Need help on working with parametric function

Here is an ODE solved by ParametricNDSolveValue solver.I got the solution. Now, I need to solve these two equations: p1 = 10 h - l; p2 = 10 h1; where ...
6
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2answers
193 views

Solving a steady-state viscous Burger's equation with NDSolve

A steady-state viscous Burger's equation is given by $$ u\,u'=\nu \,u'', \quad x\in (-1,1), $$ $$ u(-1)=1+\delta,\quad u(1)=-1.$$ Here $\nu>0$ is the viscosity, $\delta>0$ is a small ...
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0answers
45 views

Solve the Schrödinger equation of a RF-SQUID

I'm trying to solve a time-indipendent Schrödinger equation. This is the Hamiltonian: $H=E_Cq^2-E_J\cos(2\pi\varphi)+\frac{E_L}{2}\varphi^2$ (assume $E_C=1$) where $q=-i\frac{d}{d\varphi}$ and: $U(\...
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36 views

solution of a coupled differential equation with variable

I have written a code of a set of a differential equation and for one of the variables in the differential equation I have written set of another differential equation how should I call it in the ...