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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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Automatic parallelization of vector ODEs?

I read that if an ODE dX/dt=F[t,X} where X and F are vectors, is written in a vector form, the computation will be parallelized automatically. Thus I did no explicit parallelization in my Mathematica ...
Dmitry Garanin's user avatar
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0 answers
131 views
+100

Plot the solution of a differential equation

Consider: $$\frac{1}{(1-e)^2 w}=v-z$$ where $v=f(e,i,L,W,a,n)$, $z=g(e,i,L,W,a,w,n)$, and $L = h(e,w,a,b)$ are given functions. From the above equation, $e$ can be derived as a function of $w$ along ...
ppp's user avatar
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Transform a set of nonlinear equations in state space form

I have to solve a multi-body dynamic problem numerically in Matlab. The set of equations has been computed in Mathematica. To solve it in Matlab i have to transform it into state space representation. ...
Marilace's user avatar
5 votes
3 answers
208 views

Singularity or stiff system suspected in ODE that shouldn't have a singularity in the solution range

I am trying to numerically solve the following ODE where I know the value at p[1000]: ...
ydd's user avatar
  • 3,937
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Why is NDSolve misreading a standard initial value problem for a first order system of ODEs as a system of delay ODEs? [closed]

I am attempting to solve an 80-dimensional system of ODE's with standard initial conditions using NDSolve. I'm getting the error: NDSolve::cdelay: The method currently implemented for delay ...
JR6873's user avatar
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2 votes
1 answer
234 views
+100

Numerical Simulation of a Damped, Driven Nonlinear Wave System with Spatially Extended Initial Conditions

I am working on a project that requires creating a specific type of graph, but I am having trouble writing the correct code. The graph should look similar to the one I have attached below. Could ...
Athanasios Paraskevopoulos's user avatar
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0 answers
56 views

I want to plot a system of coupled pde where coefficients are component of vector defined piecewise [closed]

I am trying to reproduce some results of a paper. But I'm very new to Mathematica. I have written the code using some AI tools. but I'm unable to spot the error and mistakes in my code. here is my ...
Ashish K's user avatar
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52 views

How to make StreamPlot skip regions which gives complex results or can not be evaluated for some reason?

Many times when using StreamPlot it is hard to guess the correct limits to give it which does not result in blank plot or even the command not evaluating at all. ...
Nasser's user avatar
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40 views

Solving a second order pde from solution of another pde

I have solved the following pde numerically using NDSolveValue. ...
questionerno8's user avatar
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56 views

Boundary сonditions specified in different domains

I am modeling mass transport phenomena involving convection and diffusion within a two-dimensional box. The box has a height ranging from 0 to h along the y-axis and is divided into two domains along ...
LUIS MORALES's user avatar
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Solving a diffusion equation in a partially noisy potential

So recently I tried modelling diffusion over the rough part of a potential W. To do so I try numerically solving the Fokker-Planck equation: $$\partial_t P(x,t) = -\nabla\cdot J$$ $$J= -D(x)\nabla P-D(...
IronicOwl's user avatar
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1 vote
0 answers
51 views

How to constrain two PDE variables to be the same value on boundary?

I have a 4 pdes for 4 variables: v, v2, ua, and p. I would like to specify that v==v2 on the left and right boundaries at all times. Here are the equations: I discretise the system using PDEtoODE. ...
Ariana Fenris's user avatar
1 vote
1 answer
74 views

Coupled pdes with two different derivatives

Can someone please help me with solving the following coupled equations for $m(x,t)$, $p(x,t)$, and $u(x,t)$, in an interval $0<x<5$? I found it very hard as the second equation has both x and t ...
questionerno8's user avatar
0 votes
2 answers
101 views

Fixed coordinate is shifting in each frame of the animation

I am trying to animate a rotating coordinate system around fixed cartesian coordinates. The fixed coordinate system keeps shifting in each frame as the rotating coordinate system rotates. I am ...
SanGu's user avatar
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1 vote
1 answer
131 views

2D momentum type equation for compressible fluids

I have this program which displays errors in the declaration of terms, I've tried to modify it several times but it displays the same errors, apparently in the declaration of the term $(v \cdot \nabla)...
Kamal Khalil's user avatar
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0 answers
112 views

Animation of Euler top

I am trying to animate the motion of the Euler top, where the ellipsoid will change its Euler angles with time. Is there a method to visualize the ellipsoid's spin, nutation, and precession motion? I ...
SanGu's user avatar
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2 votes
1 answer
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A first order differential equation: Inconsistent solutions by two approaches

Assuming $a>0,b>0,c>0$, in matrix A = {{a - I*b, c}, {c, a + I*b}}; I am interested in solving the following differential equation $\frac{d}{dt}R(t) = -i(...
phy_std's user avatar
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1 vote
0 answers
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Why is NDSolve ignoring two PDEs out of three ones I am solving?

I am solving the following coupled system of 3 PDEs modelling a 1D membrane coupled to a 1D fluid flow field underneath. However, on putting them into NDSolveValue (and trying with FEM), it says the &...
Ariana Fenris's user avatar
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0 answers
26 views

Using absolute values as initial conditions

I have a system of equations I want to solve using NDSolve, which is ...
Jules Alvarez's user avatar
1 vote
0 answers
105 views

Implicit Runge Kutta for system of ODEs [closed]

I am trying to build a module that solves a system of ODEs using the implicit Runge-Kutta method but it seems that I have an issue with the convergence condition. Where might the problem be? This is ...
Elis's user avatar
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0 answers
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Stabilise equations for motion of Inextensible string subject to spatially non-uniform forces

I would like to simulate the motion of an inextensible membrane in 1D as an inextensible string subject to spatially-dependent body forces. For now, I would like it to be constrained at both ends. I ...
Ariana Fenris's user avatar
0 votes
1 answer
36 views

How to eliminate part of a linear ODE Mathematica solution that diverges for some values of the independent variable

I have the following linear ODE for which I want to find solutions that do not diverge for any value of $\theta$ with $0\le \theta \le \pi$ :$$T_n''[\theta]-\cot[\theta] T_n'[\theta]+n(n+1)T_n[\theta]=...
Bobster's user avatar
  • 143
2 votes
1 answer
75 views

Moving all terms with dependents variable to one side of differential equation

This question came up in the Maple forum: Given a differential equation, how do we move all terms with the dependent variable and all its derivative to the left side of the equation and all terms ...
Nasser's user avatar
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55 views

Solve system of integrated differential equations

I want to solve a system of integrated differential equations but I am encountering a problem with my Mathematica code. \text{ka}=\text{kb}=1; \text{wa}=\text{wb}=\frac{w}{2}; \text{Jxy}=0.5; \text{Jz}...
Radia B's user avatar
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5 votes
2 answers
217 views

How to obtain this solution to this nonlinear IVP second order ode?

This problem from Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963, Chapter 8. Special second order equations. Lesson 35. Independent variable x absent, Exercise 35.18, page ...
Nasser's user avatar
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0 votes
0 answers
56 views

Differential equation with list of functions

Let's say I have a list formed by 2 functions dependent on the variable t. For example: A[t_] := {{Exp[t] + 3}, {t^2 - 5}} I want to solve a differential equation ...
Gabriele Stevanato's user avatar
3 votes
1 answer
62 views

Solving a first order linear matrix differential equation

I am struggling in solving the following differential equation (with B and g real numbers) ...
phy_std's user avatar
  • 143
0 votes
1 answer
63 views

Vortex beam profile plot [duplicate]

I want to plot this type of plot for the Lagurree Gaussian beam $\begin{aligned} u(r, \phi, z)= & C_{l p}^{L G} \frac{w_0}{w(z)}\left(\frac{r \sqrt{2}}{w(z)}\right)^{|l|} \exp \left(-\frac{r^2}{w^...
Himani Juneja's user avatar
1 vote
0 answers
63 views

Numerically solving coupled 2rd ODE with tiny numbers

I am solving the initial value problem of two coupled ODEs numerically. The equations are ...
Link's user avatar
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1 vote
0 answers
85 views

DSolve/NDSolve two simple beam DE, left/right far pin end/connection joint continuity-error NDSolve called with two arguments; thre+ argument expected

I was able to get code for a single simply supported uniform loaded beam DE working fine. Now I tried to expand to 2 connected uniform loaded beams, no solution is reached. I attempted to define BC ...
SAK's user avatar
  • 11
1 vote
0 answers
73 views

Double pendulum with symplectic Runge-Kutta option for NDSolve not working

I would like to use the Symplectic Partitioned Runge-Kutta integrator from Mathematica to solve the nonlinear double pendulum equations. I set up the problem by first calculating the Hamiltonian ...
Meclassic's user avatar
  • 1,015
4 votes
1 answer
176 views

Kernel quits while using ParametricNDSolve

I'm trying to reproduce the plots (Figure 1 and Figure 2) of this paper. The plots are obtained by solving the Eqs. 4.3 and 4.4. The boundary conditions described in section 3.3 for Eqn. 4.3 are ...
Entangled Quark's user avatar
2 votes
1 answer
92 views

Fitting data to a system of ODE using ParametricNDSolveValue

I am trying to create the following code to fit data to a system of ODE. ...
shewlong's user avatar
3 votes
2 answers
140 views

Plotting Phase Portrait of Duffing Equation

I study a paper that describes a stationary problem where the function $\Phi_d$ satisfies the boundary conditions and is governed by a modified Laplace equation with a non-linear term. Here's a ...
Athanasios Paraskevopoulos's user avatar
2 votes
0 answers
96 views

How to solve electric drift and diffusion PDE using `NDSolveValue`?

I am trying to learn how to use NDSolveValue with various boundary conditions. After going through several examples here, I thought I'd try it on what I thought ...
BeauGeste's user avatar
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0 votes
0 answers
67 views

How to solve this partial differential equation with integral and complex value, which is the updated previous questions?

how to solve the PDE below? It is similar to previous ones I asked, but updated and simplified. I am trying to solve the PDE equation D_t(wP+wL)=D_z(S)+wJ to obtain ...
sixpenny's user avatar
  • 149
4 votes
1 answer
209 views

Is there any way to get DSolve to provide trivial solutions?

When trying to solve DSolve[{x''[t] + x'[t] == x[t] y[t], y''[t] == -x[t] y[t]}, {x, y}, t] Mathematica returns the input. Two solutions (trivial) are $$(x(t),y(...
Moo's user avatar
  • 3,334
2 votes
1 answer
85 views

How to solve the integro - differential equation with complex value involved?

I am trying to solve the PDEs which contains Integro-differential and complex values. For example, the following PDE can be easily solved. ...
sixpenny's user avatar
  • 149
3 votes
1 answer
107 views

Why does singular solution not satisfy the ode?

Should not singular solution also satisfy the ode itself? Since it is a solution. Why does Mathematica V 14 in this example generate a singular solution which does not seem to satisfy the ode itself <...
Nasser's user avatar
  • 145k
0 votes
0 answers
36 views

NDSolve does not satisfy initial and boundary condition

I am using NDsolve to solve for a coupled pde system $vA[x,t]$ and $vU[x,t]$. I have initial condition for $vU[x,0]=2$, and the boundary condition as $\partial_x vU(0,t)=1$. I have accounted for these ...
questionerno8's user avatar
1 vote
0 answers
39 views

Solution to NDSolve changes when variable range changes?

I am trying to use NDSolve to find a solution to a differential equation for $u[t]$ that should asymptote to a particular value $u_0$ as $t$ goes to negative infinity. This is a very unstable solution ...
octonion's user avatar
  • 141
0 votes
0 answers
63 views

NDSolve::litarg error and overdetermined system error in NDSolve

Before the long description about my problem, my question is How can I avoid NDSolve::litarg error and overdetermined system error in a NDSolve for simultaneous differential equation. Nowadays I ...
chickenstick's user avatar
1 vote
1 answer
67 views

Retrieving only first function in matrix ODE using NDSolve

I have a very stupid question, but I don't use Mathematica very often, so here it goes: I'm trying to solve some "matrix" ODE using NDSolve. The matrix in ...
user3914956's user avatar
1 vote
1 answer
90 views

NDSolve fails first order ODEs, but works when transformed to second order [duplicate]

The short version is that I am trying to solve a relatively simple system of coupled first order ODEs with NDSolve in Mathematica 12.1.1.0 on Windows. This system ...
Alexander Erlich's user avatar
3 votes
0 answers
68 views

Inconsistent solutions in two representations

Consider the following differential equations: ...
phy_std's user avatar
  • 143
0 votes
0 answers
28 views

NDSolve does not take into account the boundary condition

I am using the following script to solve a coupled pde. I get the error "NDSolve has computed initial values that give a zero residual for the differential-algebraic system, but some components ...
questionerno8's user avatar
0 votes
0 answers
68 views

What is the problem in the follwing code for plotting Poincaré Sections with DDE

I want to plot the Poincaré Sections for the given DDE. Kindly suggest what mistake I made in the following code? ...
Udichi's user avatar
  • 559
0 votes
0 answers
42 views

Solving system of coupled pdes with Neuman and Drichlet Bc

I am trying to solve a system of coupled PDEs. However, I have issues assigning initial and boundary values to the unknown field. I have checked and initial values satisfy the boundary conditions, and ...
questionerno8's user avatar
2 votes
1 answer
130 views

Bifurcation Diagram for Wang-Chen System

I am trying to construct a bifurcation diagram of the system $$dx/dt=yz+a,\quad dy/dt=x^2-y, \quad dz/dt=1-4x.$$ I've scoured the internet for pre-made bifurcation diagrams and found many (mostly of ...
M.S's user avatar
  • 21
0 votes
2 answers
106 views

Solution of system with some oscillations

I have already done the phase portrait of the following system: $$x'=y,y'=-y-x+x^2$$ and I want to plot it. It should be something like this (so that it must be decreasing with some oscillations
RIM's user avatar
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