Questions tagged [differential-equations]

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

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Simplifying an ODE in Bessel notation

I have the following Mathematica code: eq[r_] = 3 (1 + 2 a) g1 r y[r] - 2 (2 y'[r] + r y''[r]); DSolveValue[eq[r] == 0, y[r], r] This gives me the ...
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How to use mathematica for differential geometry

I would like to learn how to efficiently use mathematica for differential geometry and tensor analysis. I googled it and mostly found some old references to packages. I wonder if there is a good ...
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I have the system $$x' = x^2$$ $$y'= y(2x - y)$$ We can calculate the nullclines by solving the first equation for $y$, but since there is no $y$ it is just $x=0$. For the second equation, we get the ...
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Not able to plot embedding diagram of wormhole

I'm trying to reproduce the embedding diagram of the wormhole given in Fig. 3 and Fig. 4 in the article https://arxiv.org/pdf/2407.05111. I'm having trouble numerically integrating and reproducing the ...
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Splitting method for PDEs

Splitting methods are widely used for Multiphysics problems. I found a few ODE examples in Advance documentation for NDSolve. I wonder whether any such methods are available for coupled PDE systems. A ...
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Boundary condition for heat equation in polar coordinates deduced with L'Hôpital's rule fails for method of lines, but works well for FDM

Update I manage to find a way that resolves the problem. I'd like not to make this solution public for the moment so other answerers will have more chance to get the bounty. Here's a hint: it's a ...
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How to define a PDE on the boundary(only) of a domain such that it is coupled to another PDE inside the domain? [closed]

I mean where a species can be absorbed ,..etc on the boundary and diffuse along it
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NDSolve can't find Neumann Value on domain

Trying to solve for the temperature around an axisymmetric thin disk. Edges of the domain are DirichletConditions which work fine, but the solver can't find the <...
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1 vote
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I want to plot the group delay of the following mathematica code but it takes too long time

I am working on a Mathematica project where I want to plot the group delay. The problem is this code is running too slow. Is there any possibility of speeding up the code? Here is the original code: <...
340 views

Why this call to DSolve gives this error in V 14.1?

Also reported to Wolfram support just in case. [CASE:5167904]. Is there a way to correct this error from the new version of Mathematica 14.1? I do not know what changed and what is wrong: ...
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FindRoot[NDSolve...] [duplicate]

I have a function OdvodNaPolu: $\mathbb{R}\to\mathbb{R}$, and I want to find its zero. The function contains NDSolve and based ...
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1 vote
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Boundary condition error with 2D Poisson equation

I'm trying to solve Poisson's equation for the temperature difference ($\Delta T$) between two layers with known conduction between them. The layers have conductive elements spaced in a hexagonal ...
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Getting around inconsistent boundary/initial conditions for coupled PDEs

I am trying to model + and - charges in a 1d box. I want to start out with uniform concentrations of both (2 in the code below) and then turn on an electric field so the charges separate to either end ...
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Method of undetermined coefficients for ODE

Question Find the line integral curves of the differential equation $y' + xy'^2 - y = 0$. Solution: The line integral curve of the differential equation $y' + xy'^2 - y = 0$ is of the form $y = kx + b$...
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NDSolve for two layers domain

I want to solve the following system of equations using NDSolve. where prime symbol (') denotes the derivative w.r.t. the variable y. I want to plot the result in a single graph over the domain [0,1] ...
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NDSolve gets the wrong answer! How get NDSolve to correctly solve this "stiff" equation?

Below, I am trying to solve for x[t], in a sort of complicated differential equation. In this equation, x[t] is a 3-D vector ...
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How can I know for sure if I have a singularity or not when numerically plotting solutions to ODE's?

Here's my code for what I'm working on: ...
1 vote
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Solving 2D Rotational GPE and Finding Overlap Of Solutions

I want to generate those figures (fig 2) by solving equation no 7 from this paper https://arxiv.org/pdf/1906.06327 for different rotation values (\Omega) and ...
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Solving a System of Nonlinear PDEs with Finite Element Method (from paper Materialia 1 (2018) 78–88)

I am trying to solve a system of nonlinear PDEs using the finite element method in Mathematica. The system consists of equations for vacancies (V) and self-interstitial atoms (SIAs) and corresponds to ...
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Can't get differential root to plot. What am I doing wrong?

I've been trying to solve a complicated system of differential equations. After some simplifying, I've executed the following and get a DifferentialRoot as output, but for some reason, I can't get it ...
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Mathematica is giving me an error when I try to see what the form of a DifferentialRoot [closed]

I'm trying to solve a coupled system of PDE's. After some Fourier transforming, I was able to eliminate derivatives with respect to one of my variables which allowed me to eliminate one of the ...
43 views

Reliability of DSolve to ensure existence of analytic solutions

So I've been wondering about this for a long time. Of course, Mathematica DSolve can be a monster slayer sometimes but as Mathematica as it can get, the output results usually tend to be not ...
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Issues in Reproducing Rippling Instability of Graphene using Mathematica from Physical Review B 101, 235428 (2020)

I'm attempting to reproduce the numerical model of the rippling instability of graphene as described in the paper "Physical Review B 101, 235428 (2020)" using Mathematica. Specifically, I'm ...
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NDsolve does not solve equation

I have a question for system of ordinary differential equations, because Mathematica does not give the solution. To be more specific, it does not give any sign that there is some problem. There is the ...
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Solving DAE's -

I'm trying to find the structure of degenerate stars (white dwarfs, neutron stars) using the standard equations of stellar structure and Chandra's equation of state. This is a set of DAE's: https://...
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How to Compare Discrete and Continuous Lorenz System Solutions

I wrote the following code to solve the discrete form of the Lorenz system. I would like to compare this result from the table the code below generated, with a simular table derived for the continuous ...
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