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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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POD - proper orthogonal decomposition for Reduced Order Modelling

I am trying to figure out how to perform a Proper Orthogonal composition, of which an example of the procedure and analysis are found in the following tutorial video: https://www.youtube.com/watch?v=...
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ParametricNDSolve plot following the tutorial not working (with my system)

I'm trying to simulate the following system: $X'_1=a\frac{X_1^{0.4}}{X_2^{0.15}}-X_1^{0.2},$ $X_2'=X_1-X_2^{0.2}$ $X'_1(0)=X'_2(0)=1$ I simulate the system with the following code: ...
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53 views

4th order elliptic PDE

I want to analytical Solve or numerical solve by Mathematica a PDE and get a general solution in a rectangular domain? $$\frac{\partial^4U}{\partial x^4}+\frac{\partial^4U}{\partial y^4}=0,$$
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32 views

Normal form for Hopf bifurcation

I'm trying to obtain the normal form for the Hopf bifurcation using mathematica. I was looking at the following article: downloads.hindawi.com/journals/sv/1995/581272.pdf and I´ve tried to solve (25)...
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72 views

DSolve for ODEs with terms like $ y^2(t) $

Mathematica does not give me any solution for the ODEs as follows: ...
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3answers
180 views

Inhomogeneous Neumann boundary conditions for diffusion equation

I am new to Mathematica and I have a problem specifying Neumann boundary conditions in diffusion equation. The best result I managed to get is this. ...
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0answers
50 views

stick-slip oscillator: Missed WhenEvent

Using Mathematica I try to modell the stick slip effect as recommended in the documentation (WhenEvent). The initial condition starts from a state ...
4
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1answer
176 views

Dynamic, nonlinear, damped Euler–Bernoulli beam equation

I would like to solve the 3 coupled PDEs describing a damped, nonlinear (i.e displacements in the $x$ direction along the beam need to be considered along with the $y$ displacements normally ...
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0answers
33 views

Finding the Period of a Complex Solution of NDSolve [on hold]

I'm trying to solve a complex ODE with NDSolve and by plotting the solutions I can see that some of its solutions are periodic. I was wondering how can I find the period of these complex solutions? I ...
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3answers
90 views

How to plot the phase portrait of this non-linear system of ODEs

I am trying to plot the phase portrait of the following differential equation $$ \begin{cases} \dot{R}= aR+bJ\vert1-J\vert+f(t)\\ \dot{J}= cR\vert1-R\vert+dJ, \end{cases} \quad f(t)=5\sin(\pi t). $$ ...
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41 views

How to get rid of the discontinuities in the plots and animation?

Trying to plot the angles for a double pendulum against each other such that they stay within the bounds of -Pi to Pi. The NDSolve solves the equations such that if a pendulum does a full loop the ...
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1answer
61 views

What is wrong with my code? [closed]

What is wrong with my code below ...
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1answer
53 views

gradient of Legendre polynomials

I need help to check my code if my way to generate the gradient of a function that contains Legendre polynomials is correct or not. if f is a function in θ and κ ,I need the gradient of f with ...
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0answers
27 views

Problems with NDSolve, have a problem of reducing Numerical errors

I am trying solve differential equation subject to boundary condition. Here is my code: ...
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1answer
39 views

How to solve this differential equation using mathematica

I have a following differential equation where w is a function of x alone , a , b c, d,e, k, m, qi's are the constants. How to solve this in mathematica. I used DSolve but I did get any thing in ...
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0answers
33 views

Plotting gradient and newton directions for parametric system of nonlinear ODEs

I have a bucket (system) of chemical kinetics models, a nonlinear dynamical system given by: where kf >= 0 and kr >= 0 are the parameters. The initial conditions are A(0) = B(0) = 1 and C(0) = 0. I'...
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DSolveValue gives a confusing result for a simple vector-valued equation

If we use DSolveValue on just about the simplest vector ODE I can think of, it gives the following result. ...
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1answer
47 views

Real General solution of differential

For next Riccati d.e $ y' = (y^2) - 2 x^2 y + (x^4) + 2 x + 4 $ with DSolve i get Complex general solution Opres = DSolve[y'[x] == y[x]^2-2x^2*y[x]+x^4+2x+4, y[x], x] $\left\{\left\{y(x)\to \frac{...
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1answer
57 views

Non Trivial Conserved Quantity Fails To Be Conserved After Solving System of ODE's Via NDSolve

I'm trying to solve the following Darboux system of equations numerically. As a result I have the following implementation of NDSolve ...
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41 views

Solution of d.e is out from Domain of d.e

$$y'=-\frac{\sqrt{1-y(x)^2}}{\sqrt{1-x^2}}$$ ...
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2answers
181 views

Help for Solving Two Equations For Two Unknows (from a Paper)

I am trying to reproduce numerically the results found in this paper: https://ieeexplore.ieee.org/document/1707778 You don't necessarily need to read it. Basically I boils down to solving a two ...
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1answer
28 views

Is NDSolve being precise here? Light deflection angle

I am currently trying to calculate deflection angles for the path of photons near Schwarzschild black holes, using the formula $$\Delta\phi=2\int_{r_0}^\infty \frac{dr}{r^2\sqrt{1/b^2-1/r^2(1-1/r)}}$...
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System of BVP with missing BCs

I have a system of ODEs forming a BVP. In MATLAB, I can solve it with the built-in solver bvp4c. Though, this controls the final mesh itself while I would like to explicitly specify it myself. I ...
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1answer
25 views

Why does trying to plot the solution to this system of ODEs this way lead to errors?

I would like to plot the curve $\alpha(s) = (l(s), h(s))$, where $l$ and $h$ are the solutions to the system $l'^2 + h'^2 = 1$ and $l'h''-l''h'=h'\tan(l)$. Here's what I tried: ...
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2answers
63 views

Plotting solution to Differential Equation with separable variables

Got this differential equation $$y'=\frac{-x^2(y+1)}{y^2(x-1)}$$ If I try directly to DSolve it ...
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2answers
106 views

Symbolic solution for the energy of potential flow

I have a question to a physical task in Mathematica. We have this equation of motion: $$m\cdot\ddot{x} = -m(\omega_0^2\cdot x+(\epsilon x^3))=-\frac{d}{dx}V(x)$$ For energy of masspoint there is ...
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1answer
56 views

The best way to plot General solution of differential equation in shape of Inverse Function

Differential equation which solve by separation of variables. $$ y'=\frac{x^3e^{3y}}{e^{2x}(4-y)^3} $$ ...
3
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1answer
131 views

Eigenvalues of a non-Hermitian complex periodic potential

I have an eigenvalue problem: $$-\frac{d^2}{dx^2} \psi(x) +V(x)\psi(x) = E \psi(x)$$ where $V(x)$ is a complex periodic potential: $$V(x) = 4[\cos^2(x) + i 0.3 \sin(2x)]$$ It has been claimed that ...
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1answer
75 views

Complex shape of general solution of differential equation [closed]

I am abit confused, in my definition for General Solution (definition which we used on Universitet) it say's for " $C \in Reals $ " and ever when i solving ordinary differential equation of first ...
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1answer
71 views

Is there any way to save time using of “Cross” or “Table”?

I need to solve a equation by NDSlove, so I write the equation first, but it takes me a lot of time. The follow is my code ...
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3answers
80 views

Wronskian, differentials equations [on hold]

How can I in Mathematica find the Wronskian for two piecewise functions $$ \begin{align} \varphi_1(x) &= \left\{ \begin{array}{cl} -x^3 & x \in [-1,0], \\ ...
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1answer
106 views

Cat catch mouse , application of differentials equations

Can anyone help me with this: We have a room 4 metres deep and 4 metres wide. In the far right corner is a mousehole. The cat starts in the bottom left corner, and the mouse starts in the top left ...
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47 views

Why does DSolve return the same DSolve expression?

I am trying to find the closed solution for the classic chemostat model with one species and one resource (Monod response) using the DSolve() function. However, after running for 10 minutes, I get ...
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1answer
70 views

EDP exotic boundaries condtions

I'm trying to numerically solve Laplacian(V(x,y)) = 0 on a cross having Dirichelet conditions on two opposite borders (e.g. V(0,x)=-10 and V(5,y)=-10) and having dV(x,y)/dx = const . dV/dy for ...
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NDSolve:Method of Lines: Spatial Discretization: bother doing it explicitly or just implement as internal routine?

My question is whether one's code must always contain the actual description of spatial discretization written explicitly or whether the Method of Lines can be called as an internal routine. If so ...
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3answers
83 views

ndsolve with multiple initial conditions

I am trying to solve a PDE using the NDsolve with initial and boundary conditions, ...
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2answers
86 views

Issues With WhenEvent in PDEs

I am trying to solve the PDE below: ...
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1answer
64 views

Solution of differential equation and then draw a graph

I have two differential equations: $da/dt = a (.3 a^{-3} + .7)^{1/2}$ and $d \tau /dt = 1/a$. The initial conditions are $t = 0$; $a = 1$ and $\tau = 0$, respectively. How can I solve the ...
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1answer
42 views

Animate a graphics with derivative function that gathered from NDSolve

I'm defined W[t] and Q[t] like below. This code is an example that shows my problem. My real code is very long and complex that i cant make change in it. I solved my differential equations but sum ...
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1answer
30 views

D.e which solving with parametrisation

I want to solve next d.e which can be solved with parametrization (that classification group). $$y'^3-4xyy'+8y'^2=0$$ ...
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1answer
79 views

ODE which can be solved without parametrisation

I want to solve the following differential equation, which can be solved without parametrisation $\qquad y^2y'^2-2xyy'=x^2-2y^2$ I need the solution for my student research project. When I try to ...
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0answers
33 views

How to solve this differential equation

I got this DSolve[k1*y''[t] == k2*y'[t] - k3*Sin[y[t]], y[t], t] But when I try to run it there is a error: "Solve::ifun: Inverse functions are being used by ...
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4answers
382 views

Can't plot DSolve's solution to Riccati differential equation

DSolve gives a strange solution for the Riccati differential equation $ y' = (y^2) - 2 x^2 y + (x^4) + 2 x + 4 $ ...
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1answer
68 views

NDSolve:PDE system, initial-boundary value problem:warning:NDSolve::mconly: For the method NDSolve`IDA, only machine real code is available

I tried to NDSolve the PDE system $$\partial_t w =x\cdot w\quad\quad\partial_z x=w$$ for $$(t,z)\in[0,1]\times[0,\pi]$$ with boundary conditions $$x(t,0)=w(t,0)=w(t,\pi)=0$$ and initial conditions $$w(...
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0answers
27 views

Domain of differential equation

I made some function for plotting Domain of differential equation , will show how it works for $y'=\frac{\sqrt{1-x^2}}{\sqrt{1-y^2}}$ ...
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2answers
140 views

NDSolve:Coupled PDE's, initial-boundary value problem: unreasonable “insufficient number of boundary conditions” error

I tried to NDSolve the PDE system: $$\partial_t y = x\partial_z w \quad\quad \partial_t w = \partial_z y \quad \quad \partial_z x=w $$ for $$(t,z)\in[0,1]\times[-1,0]$$ with initial conditions $$x(...