# Questions tagged [differential-equations]

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

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### 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 ...
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### 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: ...
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### 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 ...
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1 vote
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### 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 ...
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### 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 ...
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### How to get a stable solution of diffusion-convection PDE, while don't make to 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 ...
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### 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: ...
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### 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: ...
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### 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 ...
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### 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 ...
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### 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....
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### 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 ...
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### 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: ...
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### 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 ...
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### Finding roots of fluctuating polar function

EDIT1: Whenever the self intersecting curve intersects the x-axis, How are roots of this cyclic function found ? ...
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### 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: ...
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### 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 ...
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### 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 ...
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### Fractional PDE with CaputoD

I'm trying to solve this fractional PDE ...
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1 vote
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### 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, ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...
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### 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 ...
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### 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, ...
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### 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: ...
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### confused by integration constants in DSolve

I am trying to solve the following coupled differential equations using DSolve[] which has code ...
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### 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? ...
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### Is it really possible to use ExperimentalOptimizeExpression 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 ...
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### 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....
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### 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: ...