Questions tagged [differential-equations]

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

Filter by
Sorted by
Tagged with
-2 votes
1 answer
54 views

Finding correlators for a solution of NDSolve

I want to find correlations for a function $x(t)$ between pairs of times $t_1$ and $t_2$ i.e. to possibly get a functional form or fit for $\langle x(t_1)x(t_2)\rangle$. This function $x(t)$ is ...
user avatar
  • 1
0 votes
1 answer
63 views

DSolve general solution constants setting

The Mathematica Documentation reference for DSolve (https://reference.wolfram.com/language/ref/DSolve.html), subsection Scope/Hyperbolic Partial Differential Equations, contains an example: ...
user avatar
  • 3
0 votes
0 answers
45 views

Solve System of Differential Equations using a Table with two variables

I'm trying to solve a system of differential equations, using Table to define the equations I want to solve. I managed to do it with a table with one index, as there is an example in the docs, but I ...
user avatar
  • 13
1 vote
0 answers
21 views

NDSolve error in Functional Delay Diff Eq

I'm trying to use Mathematica to study an equation that has an unusual dependence on past states, i.e. some kind of a Delay Diff Eq. For the sake of this post, we can say that the equation I would ...
user avatar
  • 203
0 votes
1 answer
44 views

Simulating/solving a Langevin equation with overdamped dynamics and plotting a phase space plot

I've been reading about the Langevin equation, specifically the case where we are dealing with overdamped dynamics. I'd like to simulate the dynamics discussed in the second link and effectively ...
user avatar
  • 2,352
4 votes
0 answers
94 views

Solve 3D convection-dominated PDE with discontinuous coefficient, without tiny mesh

I'm trying to simulate a self-propelled particle diffusing on a disk. The direction of the self-propelled velocity $\vec{v_A}$ doesn't change, while it speeds up at the boundary and slows down at the ...
user avatar
0 votes
0 answers
43 views

Why do I get different result when trying to solve the same problem with one Solve and two Solve?

first way which gives out the result very quickly: ...
user avatar
  • 111
0 votes
0 answers
38 views

How can I solve this given Partial Differential Equation (PDE)?

I build this PDE from the physics, the equation and the value of all parameters are like this: ...
user avatar
0 votes
1 answer
64 views

How to optimize code for obtaining large data set?

In an application, I need to find a region where some conditions must be true. However, these conditions are made of interpolating function solved by ParametricNDSolve. I will give a toy model example ...
user avatar
  • 1
3 votes
1 answer
129 views

Dsolve cannot solve this nonlinear ODE system

when I run this, I get "Supplied equations not differential or integral equations of the given functions" although the solution for this initial conditions is x = [sin(t),0,cos(t),0]. Why ...
user avatar
0 votes
0 answers
46 views

Using DSolve, For A System With A Piecewise Function, And For Given Boundary & Continuity Conditions

I'm trying to solve a system of ODE's, analytically, to find the integration constants. The system is the following (with zUpper=125 000 and zLower= 200 000). For 0 <= z <= zUpper: 3 T''[z] == 0....
user avatar
2 votes
1 answer
80 views

Solving 2D Coupled Nonlinear SO Coupled Equation

I am trying to solve coupled nonlinear SO coupled equations in 2D from the following two papers https://arxiv.org/pdf/2105.08849.pdf and https://arxiv.org/pdf/2109.00491.pdf. They have given an input ...
user avatar
0 votes
0 answers
50 views

How to obtain Potential from Action?

I am trying to reproduce the Potential from the equation (29) for B=1 from this paper (Page 14) I have obtained the Equations of motion from the Lagrangian by using the code given below: ...
user avatar
  • 313
1 vote
0 answers
33 views

Why does Mathematica seem to give this `DSolveDispatchODE` error seemingly at random with `DSolve` despite working

I have tried the following 4 test cases for DSolve: Gives correct solution with DSolveDispatchODE error ...
user avatar
  • 707
-3 votes
0 answers
77 views

Finding roots of fluctuating polar function

EDIT1: Whenever the self intersecting curve intersects the x-axis, How are roots of this cyclic function found ? ...
user avatar
  • 2,820
2 votes
1 answer
62 views

Lyapunov exponents at a fixed point

I am trying to find the Lyapunov exponents at a fixed point as given in the paper here(page 14). The code that I have used till now is given below: ...
user avatar
  • 313
3 votes
2 answers
162 views

Need help to speed up the Gaussian quadrature

I am trying to compute the $L_2$-norm of the solution $y(z,t)$ of a PDE with Gauss quadrature using the following code, where $z$ is space position and $t$ is time, then to construct it as a function ...
user avatar
  • 723
7 votes
2 answers
230 views

Numerical solution for a non-linear Fractional Differential Equation (FDE)

As shown below, a neat explicit expression is obtained for F=2, however an exact solution is not present for 1< F < 2. How do we obtain numerical values for F = 1.5 (for instance)? There have ...
user avatar
  • 3,014
5 votes
1 answer
186 views

Fractional PDE with CaputoD

I'm trying to solve this fractional PDE ...
user avatar
1 vote
1 answer
60 views

NDSolve issue with summation

I have the following equation I am trying to plot, $r''=f(r)+\sum_{n=1}^{\infty}a^n \frac{d^n}{dt^n}(f(r))$ and $r$ is a vector in $(x,y,z)$ that are time dependent. I wrote the code as follows, ...
user avatar
  • 755
5 votes
2 answers
184 views

Is it possible to characterize the sign of the trace and det at the fixed points of a dynamical system using Gröbner, postponing computing the points?

Here is an example of a dynamical system for which the isoclines may intersect at two or more points (under certain numeric conditions). It is easy to compute the trace and determinant of the Jacobian ...
user avatar
  • 1,110
2 votes
1 answer
93 views

Analytical Solution vs NDSolve. How to find agreement? [closed]

I have an ODE to which I know the solution. When using NDSolve to find the same solution, the result doesn't agree with the analytical solution. I am looking for advice on what I could try modifying ...
user avatar
  • 21
5 votes
1 answer
148 views

Limit cycles and phase portraits of a two-dimensional polynomial quadratic systems using Mathematica

Cross-posted: https://community.wolfram.com/groups/-/m/t/2589679 I have elementary questions about the construction of phase portraits and limit cycles using Mathematica. It should be remarked that I ...
user avatar
5 votes
1 answer
192 views

Monte Carlo Simulation of Charged Particles in Non-Uniform Electric Field

I have a code (provided below) which simulates the motion of an ensemble of charged particles which are subjected to a complex static electric field which passes through some aperture in a metallic ...
user avatar
  • 353
6 votes
2 answers
122 views

Why is DSolve unable to solve this second order ode with initial conditions? Any workaround?

Fyi, report to WRI as suggedted. [CASE:4956902] This ode is similar to one here but for some reason DSolve could not able to solve this. This ode is from a ...
user avatar
  • 112k
3 votes
1 answer
66 views

How did DSolve solve for the constants of integrations in this ode?

I solved this ode by hand and obtained the general solution. But not able to solve for the constants of the integrations given the initial conditions, as when I try, I get no solution. Yet, ...
user avatar
  • 112k
0 votes
1 answer
71 views

Numerical solution of differential equation with DiracDelta fit boundary condition at zero poorly

I need to solve: $x^2y''(x)+(2x+1)y'(x)-x^2\omega^2y(x)=\frac{-\omega^2\delta(x-x_0)}{4\pi},x\in[0,\infty)$ with boundary conditions:$y(0)=1,\ y(\infty)=0$ , $\omega$ is a function of this form: ...
user avatar
0 votes
0 answers
57 views

confused by integration constants in DSolve

I am trying to solve the following coupled differential equations using DSolve[] which has code ...
user avatar
  • 2,735
0 votes
0 answers
60 views

streamplot for differntial equation

how I can use StreamPlot or VectorPlot to show x[t] and 1-x[t] and show convergence point in my plot with a different colour like a blue point? ...
user avatar
  • 55
2 votes
1 answer
121 views

How to solve Neumann boundary ODE with shooting method?

$\rho(x)$ is the distribution function. I'm trying to solve the following equation: $D_t\frac{\partial^2\rho}{\partial x^2}-\frac{\partial (v_0\rho)}{\partial x}=0$ $D_t\frac{\partial\rho}{\partial x}-...
user avatar
2 votes
2 answers
270 views

Bizarre solutions of a first order PDE

DSolve[{x y D[u[x,y],x]+(x-y)y D[u[x,y],y]+x==u[x,y],u[x,0]==x},u,{x,y}] returns unevaluated. Removing the initial condition: ...
user avatar
2 votes
1 answer
79 views

How to solve PDEs for function $\Psi(z,\bar{z})$ dependent on independent variables $z,\bar{z}$? (Wirtinger derivatives)

For the past few days, I have been struggling to convey to mathematica to solve a PDE that is in terms of the independent variables $(z,\bar{z})$. I know mathematica supports solving PDEs with respect ...
user avatar
2 votes
1 answer
38 views

Plotting from NDSolve [closed]

Code: ...
user avatar
  • 287
1 vote
1 answer
49 views

Using RegionPlot and NDSolve to plot areas of species coexistence across 2 parameter space

I have four ODEs corresponding to four species: ...
user avatar
  • 13
10 votes
4 answers
770 views

Plot a phase diagram

I am trying to draw this system of differentiable equations, whose phase diagram is: found in the following article. I am new using Mathematica, I was guided by these posts: 1 and 2. But I get an ...
user avatar
  • 203
1 vote
1 answer
95 views

How to set a adiabatic boundary conditions for a convection function?

$\rho(x,t)$ is the probability function, $x\in[-1,1]$. I'm trying to solve the convection function with adiabatic boundary condition as follows: $$ \partial \rho/\partial t=D_t\frac{\partial^2\rho}{\...
user avatar
1 vote
1 answer
69 views

Issues using DSolve to solve system of differential equations

I know there are a lot of similar questions to this, but I am relatively new to this and the answers don't make a ton of sense to me. I am trying to use DSolve to get harmonic motion in three ...
user avatar
0 votes
0 answers
47 views

Linear Stability Analysis with Mathematica [closed]

I'm trying to apply Linear Stability Analysis to a dynamic system of two coupled PDEs. The first of these equations is given by: $$ \frac{\partial h}{\partial t} + \nabla\cdot \left[-h^3\nabla\frac{\...
user avatar
  • 211
1 vote
0 answers
32 views

Discrepancies in NDSolve Solution Between 4D and its Reduced 3D Counterpart

I have two systems, a 4D system and a 3D system. The 3D system is a reduction of the 4D system in such a way that: ...
user avatar
0 votes
0 answers
72 views

How can i draw graphical figure as contours?

I have solved a second order differential equation using Mathematica code ...
user avatar
  • 91
0 votes
1 answer
62 views

Turn a two-dimensional function with cylindrical symmetry into a three-dimensional function

Say I have a function that I solved from a differential equation in 2-dimensions because I know in advance that there is cylindrical symmetry in the solution. For instance, say we obtain the solution: ...
user avatar
4 votes
1 answer
153 views

Set Neumann Boundary Condition in NDEigensystem function

I want to get the eigenvalue and the eigenfunction of the following partial differential equation: $$ -(\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2})\psi_n (x,y) + [\frac{1}{4}(x^...
user avatar
  • 41
3 votes
1 answer
50 views

How to detect the positive solution to this logistic boundary value problem

I am trying to find the positive solution to this nonlinear ODE. Theoretically, it has been proven that this problem has a unique positive solution for lam large. But, Mathematica can detect only the ...
user avatar
  • 103
3 votes
1 answer
226 views

Semi-classical approximation of modified Schrodinger's equation on a sphere leads to ndsz warning

I know this error is very common. I checked out a good number of proposed solutions to this problem, but unfortunately, none of them helped in my case. I would appreciate any help or hints on how to ...
user avatar
  • 33
3 votes
2 answers
101 views

What bump function to use in a system of partial differential equations?

I am solving a system of three time-dependent partial differential equations on a circular domain, using the finite element method. However, in the outer part of the domain ($r>R$) the equations ...
user avatar
  • 31
0 votes
0 answers
74 views

Is it really possible to use `Experimental`OptimizeExpression to tune the equation for `ParametricNDsolve`?

I tried to implement a method of speeding-up of ParametricNDSolve proposed by @MichaelE2 in comment to my post Can I speed up ParametricNDSolve by converting ODE to ...
user avatar
0 votes
1 answer
176 views

Sticky Collisions (perfectly inelastic)

There is an awesome simulation https://mathematica.stackexchange.com/a/124926/87086 which shows N particles bouncing in a box (with elastic collisions), made by @Feyre https://mathematica....
user avatar
  • 353
2 votes
1 answer
53 views

Solving a vector diferential equation lead to ComplexInfinity Encountered non-numerical value for a derivative at t == 0

I'm trying to solve the following Vector PDE: I implemented the following code: ...
user avatar
0 votes
1 answer
88 views

How to plot a Phase-Portrait of three coupled differential equations?

I have the following problem: I would like to plot a StreamPlot (phase portrait) of three coupled, second-order, non-linear differential equations. These are: ...
user avatar
  • 3
1 vote
0 answers
82 views

Can I speed up ParametricNDSolve by converting ODE to DAE?

I use ParametricNDSolve to find a solution to a very cumbersome ODE: ...
user avatar

1
2 3 4 5
133