Questions tagged [differential-equations]

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

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NDSolve a system of PDEs with Periodic Boundary Conditions

I would like to analyse the system of differential equations $\begin{equation} \begin{split} \partial_tf_0&=\frac{C_{\mathbf{r}}}{(1+\lambda)^2}\bigg[\bigg(1+\frac{\lambda^2}{2}\bigg)\partial_{...
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27 views

How to visualize second order differential equations? [duplicate]

As we now we can use StreamPlot to visualize first-order differential equations like:y'[x]==1+x-y ...
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71 views

How to solve a system of nonlinear differential equations like this numerically

There are a set of nonlinear Bloch equations. ParametricNDSolve can not give the correct answer, how to deal with these equations? The desired answer should be (...
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1answer
83 views

NDSolve misses nontrivial solution

The initial value problem I would like to solve possesses an analytical solution ...
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1answer
117 views

Coupled pde for multiphysics joule heating with temperature dependent properties - error inconsistent dimensions

I want to simulate 3D joule heating and followed the wolfram multiphysics tutorial. This multiphysics problem is comprised of the equation for the voltage field: and the heat equation: with the ...
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Driving along a Beziercurve with given velocity

In this model I try to describe the kinematics of a point moving along a beziercurve b[u] (bezier parameter 0<u<1) with prescribed velocity ...
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1answer
120 views

Solving a differential equation where all functions are unknowns

I'm trying to solve DSolve[f[x]*(x^2*g''[x] - 2*g[x] + 2) + x*(x*g'[x] - 2*g[x])*f'[x] == 0, g[x], x] for $g(x)$, however Mathematica cannot find a solution. ...
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31 views

Errors while trying to do a change of variable

I have the following differential equation: $ \tag{1} \Delta^{-s}\frac{d}{dr}(\Delta^{s+1} \frac{d R(r)}{dr}) + (\frac{K^2 - 2 i s (r - M)K}{\Delta} + 4is \omega r - \lambda)R(r) = 0$ where $\Delta \...
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1answer
87 views

How to solve this set of integrated PDEs

Could anyone help me solve set of pdes with embedded integration? The pdes below is solvable , but can not be solved when I tried different parameters such as ...
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1answer
49 views

NDSolve Encountered non-numerical value for a derivative at t == 0

I want to solve this no-linear differential equation system: $1.2 (1 + 20(r(t)^2 + 2^2 + 4 r(t) \sin(\phi(t)))^2) \ddot\phi(t) + \dot \phi(t) + \phi(t) = 50 \sin(4 t)$ $\textbf{If}$ ($|-r(t)\dot\...
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41 views

How can I set a find max value function with parameter in NDSolve

For example, Here is a NDSolve function with a parameter of w ...
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1answer
38 views

ODE Cauchy problem [closed]

I want to prove that the followning Cauchy problem doesn't have solution: $y'(x)\sin(x)=y\ln(y),y(\frac{\pi}{2})=1$ I solved the ODE and i found: $\ln(|\ln(y)|)=\ln(|\tan(\frac{x}{2})|)+c$ When i put ...
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49 views

NDsolve taking value of previous time step

I am using de NDsolve code below: ...
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1answer
126 views

Equation of motion through the Lagrangian with Lagrange multipliers

I ask for advice, I'm a little confused. I have such a Lagrangian. $L=\frac{1}{2}m(\dot{x}^2+\dot{y}^2)-\lambda(2x^2+3y^2-1^2)$ Here $\lambda(2x^2+3y^2-1^2)$ is the constraint on the phase variables. ...
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2answers
82 views

Using NDsolve with WhenEvent is not working

I am trying to use WhenEvent in this nonlinear equation system: $\ddot r-\dot\phi^2r+9.8(\sin\phi-0.7\cos\phi)=0$ $1.2(1+20(r^2+2^2+4r\sin\phi)^2)\ddot\phi+\dot\phi+...
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1answer
52 views

NDsolve for No-Linear system getting "not a list of number" [closed]

I want to solve this No-Linear equation system: $1.2 (562500 + 1.2(r(t)^2 + 40^2 + 2r(t)40Sin(\phi(t)))) \phi(t)'' + 1030400\phi'(t) + 0.41\phi(t) =2Sin (4 t)$ $r''(t) - 0.7*9.8Cos(\phi(t)) + 9.8 ...
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1answer
174 views

DSolve fails to find solution based on elementary function

I have two differential equations for which DSolve does not find a solution, however, there are simple solutions in terms of elementary functions, and more ...
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1answer
74 views

Solve a differential system of equations in time

I am trying to solve a system of 3 equations and 3 unknown variables that change in time (Tw(t), Tcor(t), Texit(t)). ...
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1answer
76 views

How to verify series solution to an ode generated by AsymptoticDSolveValue?

To verify solution returned by DSolve, one can use the method shown in howto/CheckTheResultsOfDSolve.html and look for True (...
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2answers
77 views

Series solution to an ode does not satisfy initial conditions. Frobenius series. AsymptoticDSolveValue

I was trying to verify my solution to this ode using power series method. The expansion point is x=0. This ode has removable singularity, so Frobenius series and ...
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1answer
66 views

NDSolve unable to solve coupled ODE's after specific point

I am trying to solve a set of coupled differential equations that look like this ...
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1answer
102 views

Ordinary differential equation with variable (polynomial) coefficients -form of solution

If you have a differential equation with polynomial coefficients then quite remarkably Mathematica can find a solution. For example for the second order differential equation $ y''(t)+b y'(t)+\left(\...
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51 views

NDSolver cannot give precise result for extremely small values

I would like to solve an ODE with MMA. The equation is simply the Coulomb law. However, I cannot get a satisfying result: ...
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4answers
256 views

Any Mathematica techniques to calculate time takes to reach the equilibrium of a PDE solution

I am solving this PDE numerically (dimensions: spatial variable x and time t). I know how to solve my problem numerically (for a given range of time). The solution reaches its equilibrium after a ...
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1answer
81 views

Stiff system problems with NDSolve

I'm trying to solve the two order differential equations using NDSolve. Here is the code: ...
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159 views

How to plot poincare map as shown in below image for Duffing equation?

I am trying to plot phase diagram and poincare map. But I cannot get the poincare map as shown in the image below Phase Space ...
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102 views

How can I Plot Phase Portraits Using ParametricNDSolve function(already know about StreamPlot function)?

I have a 2nd order ODE: $$\ddot{\phi}+3\dot{\phi}\sqrt{(\frac{8\pi G}{3})(\frac{1}{2}[\dot{\phi}^{2}+m^{2}\phi^{2}])}+\phi m^{2}=0.$$ I can use the StreamPlot command by breaking the ODE into a set of ...
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48 views

I have a problem evaluating an ODE in Mathematica, where the error asks me to define a dependent variable?

I am trying to solve a series of linked ODEs in Mathematica (where the system describes the trajectory of a ball through the air). ...
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2answers
83 views

Assigning A Symbol To A Second DSolve Solution

I am looking for a way to compress a lengthy DSolve solution to a single symbol, kind of like assigning a variable. I have this expression: ...
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52 views

Supplying a seed for an iterative method in LinearSolve

Just a quick question. Does anyone know if it is possible to supply a seed for the iterative methods in LinearSolve? I have a large sparse system, and even using some Krylov iterative solver, my ...
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1answer
69 views

Matrix differential equation with DSolve doesn't work

I'm trying to solve matrix differential equation with DSolve, but I got an error. ...
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70 views

Can mathematica numerically solve this system of coupled integro differential equations?

Here's my system: R(x,y,t) is the concentration of a chemical that's diffusing across the box. The disk is a mobile sink for the chemical, which absorbs it in proportion to its concentration. The ...
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2answers
223 views

FEM 1D 3D region coupling - speed up coupling using boundary integration

I am working on a simulation of the heat equation involving a 3D solid simulation coupled to a 1D fluid simulation (convective term of heat equation). I am using the method of false transient as ...
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2answers
198 views

Show resonance with wave equation numerically

Assume I have a one-dimensional medium of length $L$ and in a ring shape. The wave propagation in the medium is described by the wave equation $\dfrac{d^2 u}{dt^2} - v^2 \dfrac{d^2 u}{dx^2}=0$, with $...
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1answer
104 views

What's a better way to handle the symmetry condition in this PDE?

This is a textbook problem, however, I'm having a hard time getting MMA to reproduce the result. The problem is a plane, incompressible flow around a circle. I am solving for the stream function, and ...
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100 views

FEM 1D 3D region coupling - integration too slow for coupling with energy conservation

EDIT: I reposted this question, removing everything that is not necessary for my coupling approach. Find the new post here. I am working on a 3D simulation of the heat equation which is coupled to a ...
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1answer
93 views

Why this Basis Parabolic PDE's solution is not smooth?

What is this Parabolic PDE modeling in real life? Why the solutions is not nice? Have I made any coding errors? $\frac{\partial u(t,x)}{\partial t}=\frac{\partial^2 u(t,x)}{\partial x^2}$ $\frac{\...
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0answers
77 views

How to calculate precise higher derivatives of ParametricNDSolve solution

Higher Derivatives of NDSolve don't match the results from DSolve solution, can I somehow increase the accuracy of numerical method to match arbitrarily high derivatives? Equation I am using ...
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1answer
136 views

NDSolve unable to solve system of PDEs

I'm trying to solve a set of PDEs and am running into problems. The system is defined by: As can be seen, there are two dynamical equations for $\rho$ and $\phi$, but the equation for $v$ has no time ...
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3answers
539 views

Routh-Hurwitz criterion not giving correct answer when done manually?

Consider the system: \begin{align} \frac{dS}{dt} &= \nu N -\frac{\beta S I}{N} + \xi R - \nu S\\ \frac{dE}{dt} &= \frac{\beta S I}{N}- \sigma E -\nu E \\[2ex] ...
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1answer
257 views

Why DSolve solution to this PDE does not match NDSolve solution?

I was answering different question How Can I Visualize a PDE Boundary Condition? and in the process, found that DSOlve solution to the laplace PDE does not agree ...
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1answer
121 views

How Can I Visualize a PDE Boundary Condition? [closed]

I want to use Mathematica to visualize boundary/initial conditions for PDEs in 3-dimensional space. This was sparked by the initial comment in this question, which attempts to solve the PDE $$\...
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1answer
52 views

use of parametric ndsolve with a constraint

I want to solve differential equation $$ \frac{y''[x]}{(1+y'[x]y'[x])^{3/2}} = -a -y[x]/ \sqrt{2} + x/ \sqrt{2} $$ subject to boundary condition $y(-1) = y(1) = 0$ for some value of $a$. $a$ is found ...
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1answer
65 views

Find Order of a Differential Equation (ODE or PDE)

In Mathematica, I need a code in order to find the order of ODEs and PDEs. Here are some examples using different notations: For fifth-order ODE: ...
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0answers
90 views

Axes ticks scaled in powers of ten

I'm trying to plot the solution of an ODE and I would like to have the ticks in powers of ten. Although, this happes automatically from Mathematica for small orders, such as ...
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1answer
98 views

Integral in NDSolve, boundary conditions and initial conditions can't both satisfied

I have serval reaction-diffusion equations to be solved. Which are equivalent to the following problem: First is a simple diffusion equation of $Z(t,r)$ like below: $$ \dfrac{\partial Z}{\partial t}=A(...
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1answer
71 views

System of PDE with integration conditions interior of domain

I am trying to solve this system of pde numerically. I am unable to find any method in Mathematica that can handle this problem. The issue is having this integration condition in the domain. I tried ...
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1answer
81 views

How do I make a second order differential equation match a difference equation?

I have fitted a difference equation to some data and would now like to find a differential equation that matches the difference equation. The difference equation and differential equation are $$ y(n)=...
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1answer
78 views

Is it possible to solve this system of ODEs using Mathematica? [closed]

I have a system of 6 1st order ODEs. Since, I don't have access to a Mathematica license yet, I have tried to solve the problem using Maxima but it failed. I have also tried Maple but it takes several ...