# Questions tagged [differential-equations]

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

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### How to apply the utility Packages for Numerical Differential Equation Solving

I have solved two coupled equations with {Solf, Solg} = NDSolveValue[eqns, {f, g}, {x, 0, L}, {t, 0, tmax}] and want to extract the computational grid ...
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### NDSolve 3D Poisson PDE (cylindrical coordinates)

I try to model the threedimensional heating problem of a flat cylinder which is heated along the circumference and cooled along the face side. The temperature ...
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### How to solve wave equation with finite elements when material properties vary continuously over a region

I am solving the one-dimensional wave equation over regions where the bulk modulus (and thus the wave speed) vary continuously over a region. The current version seems to assume that the material ...
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### NDSolve: How to perform a reverse integration consistency check?

Let there be the following NDSolve code: s = NDSolve[{y'[x] == y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}] I think it ...
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### Stiff system of ODEs

I'm trying to solve a system of differential equations with NDSolve, but I get the error message: NDSolve::ndsz: At lnP == -21.0018, step size is effectively ...
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### NDSolve: “Stiff system” error returned instead of known smooth solution

I tried to reproduce a known smooth analytical solution with NDSolve but only got ...
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### Encountered non-numerical values at (ParameticNDSolve/NDSolve)

I have the following problem: Even though I defined every other constant in the code, using either NDSolve or ParametricNDSolve, ...
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### Solving 2D convection-conduction equation via using Fourier integral transform: the disappearance of the convection term?(with code)

I am currently solving a 2D convection-conduction equation. The convection is only working on the x direction. The governing equation and its associated conditions are given as where T is the ...
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### Problem combining ParametricNDSolve with NonlinearModelFit

Final Edit: I have found a solution! Specifying Method->"LevenbergMarquardt", Gradient->"FiniteDifference" gives the behavior I am looking for. Huzzah! It appears that the crashing behavior was coming ...
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### d-dimensional compiled function in NDSolve

Based on this answer, I understand how to use a one dimensional compiled function in NDSolve. Mathematica NDSolve and 'Compile'? I'd like to be able to use a d-dimensional compiled function <...
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### NDSolve solves this ordinary differential equation only “half-way”

This system eqs = {(1/2) Y'[x]^2 == (1 - Log[Y[x]^2]) Y[x]^2, Y[0] == 1} is known to have a simple solution in terms of Gaussian functions, which can be checked ...
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### Dynamical PDE system tutorials

Which are some up-to-date tutorials or books on integrating dynamical PDE systems (involving chaos, Shock waves, etc.) with Mathematica 10.0?
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### How to solve this partial differential equation for $f$?

I want Mathematica to solve for the function $f$. $f$ satisfies the following constraints. $\frac{\partial}{\partial x} f(x,y) = y$ $\frac{\partial}{\partial y} f(x,y) = x$ $f(0,0)=0$ It would ...
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### Non-linear ODE from closed-loop system and Response

I started using Mathematica 12 and ran into difficulties. Namely, I want to compare the results of the calculation of a closed system from Simulink and in Mathematica. I rummaged around a bit on the ...
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### Solving an algebraic-differential equation

I cannot find the relevant part in the documentation. Maybe you have a quick solution to my problem. Background Sometimes you want to propagate in time some system of ODEs, but not all the variables ...
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### Update initial conditions recursively/sequentially within ParallelTable using NDSolve

I am modelling 3D motion of particles inside a force-field using second-order coupled PDEs, which I solve from time t=t0 to t=t1 with initial conditions x0,y0,z0. I have a total number of "particles" ...
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### How to solve this differential equation analytically?

How can I DSolve the following differential equation? Is there an analytical answer to this equation? ...
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### Evaluation functions with lower and upper limit ODE?

How do I find the numerical value of y at 0 and also at 1. Here is my code. I appreciate any help. ...
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### Matrix of functions

I want to create a matrix of functions. As explained in this question, I can create a matrix of variables: ...
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### 1D transport equation with Neumann conditions

I'm trying to solve 2nd order differetntial equation of heat transfer-type in a finite system x<0,L>, in particular: ...
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### Get the derivative function plot from a NDSolve solution

I been trying to plot the derivative function of j[t], being j'[t]. Here a look to the code. I would appreciate your help. Thank you ...
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### Sensitivity analysis of a hybrid system (using WhenEvent) using ParametricNDSolve [closed]

I am trying to do a sensitivity analysis using ParametricNDSolve for a hybrid system. with the following event: ...
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### DEigenvalues and NDEigenvalues return different values

In the following example, DEigenvalues and NDEigenvalues return different results despite having identical arguments. Does anyone know why? (I use Mathematica 11.3) ...
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### why DSolve in V 12 returned an internal module variables with \$ on them in this example?

Fyi, Reported to WRI in case it is a bug. [CASE:4288939] Is this supposed to happen? ...
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### Hybrid Systemn Anomalous results while using ParametricNDSolveValue

The hybrid system that I am solving ...
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### One term in non-linear equations prevents NDSolve to work

I am currently working on the stratification of the core of the planet Mercury, meaning the formation of a conductive layer at the top of the convective core, with a moving interface between both ...
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### How to vectorize this nonlinear ODE system for NDSolve?

I learned a long time ago that NDSolve can often be sped up by vectorizing systems of equations. I've got a problem now that seems ideal for this approach, but I ...
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### Cross coupling in DirichletCondition not supported — conflict with documentation?

Mathematica 12.0.0.0 happily solves the trivial coupled differential system as follows: ...
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### InverseFourierTransform takes me forever

I am trying to solve complicated PDEs using FourierTransfrom and InverseFourierTransform on Mathematica 12.0, but the code below does not give me a result. I do not get any error messages but the ...
NDSolve can be broken into three stages: NDSolveProcessEquations processes the equations and sets up an NDSolveStateData ...