Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
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Solving Maxwell's Equations in Mathematica
For the sake of demonstration (for my students) and practice, I wanted to numerically calculate the electric and magnetic field (3D) for a sphere of uniform density moving slightly to the right and ...
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DSolve breaks when the ordering of independent variables aren't proper?
Bug introduced in 3.0 or earlier and persisting through 13.2
I encountered this when trying to solve this problem with DSolve:
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How to modify NDSolve`StateData without crashing the kernel?
Probably a hard question, but it's better to cry out loud.
Reminded by Chris K, I noticed my fix function has been broken since v11.3. After some checking, I ...
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DSolve returns an answer that is not a solution
Investigating DSolve misses a solution of a differential equation, I came across this odd behavior of DSolve.
The following DSolve command returns an answer to the ...
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benchmark of Mathematica's FEM?
Does anyone have any numbers on how mathematica compares to other commercial (eg ANSYS) or free FEM softwares (eg. FreeFEM++, FEniCS, elmer)? If this is too vague say solving the diffusion equation in ...
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Precision and accuracy in NDSolve and NMinimize
I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
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Modelling Hysteresis with a Differential Equation
I want to implement the bulk ferromagnetic hysteresis model (mostly the Jiles-Atherton Model), see http://drum.lib.umd.edu/bitstream/1903/6043/1/PhD_99-1.pdf page 44 equation (30).
The needed ...
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Spurious Error Messages from NDSolve when Using WhenEvent with Time Delays
Bug introduced between versions 10.1 and 10.4, and resolved in 11.3.
Using either 11.2 or 10.4 on Windows 10 (64 bit), I am unable to reproduce the answer by March to question 99576. Specifically,
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Symbolic Weak Form
Usually I write the weak form by hand for my FEM code, but it's a little annoying and mechanic sometimes.
So, I wonder, is there any way to generate the symbolic weak form in Mathematica? For ...
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Shortest Distance between two points on a 2D surface
I am working on an interesting problem, that consists of trying to compute the shortest distance between two points on a 2D surface. This 2D surface can be represented in a 3D space by the function $f(...
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How can we improve transonic flow visualization?
With this code we can make 2D FEM simulation of transonic flow around airfoil NACA 0012 at Mach number of 0.925. It takes about 5 minutes on the XENIA-15 laptop of 32 GB memory with processor Intel ...
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Numeric Solution Hydrogen Atom
I'm trying to solve the Schrödinger equation for the hydrogen atom without made the variable separation of the polar and radial coordinate. It is my test code to extrapolate to another system with its ...
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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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Solving ODE with assumption that solution is bounded at boundaries?
For a HW problem, this ODE had boundary conditions given that are not the normal boundary conditions, instead the problem says that solution $u(t)$ is bounded at the left and right ends of the domain. ...
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Spurious DSolve Solution
Bug introduced in 8.0.4 or earlier, persisting through 13.2.
DSolve quickly returns solutions to the following PDE (which is the homogeneous portion of the PDE in ...
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GreenFunction for Helmholtz equation in arbitrary Rectangle region doesn't evaluate
Bug persists through V13.0.0 or later
Here is a basic example found in the documentation of GreenFunction:
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Where is 1/0 coming from in this call to DSolve?
Bug introduced in 11.3 or earlier and persisting through 13.1 or later
Report to WRI [CASE:4246236]
This is using 11.3 on windows 10.
This is a pde from Handbook of first order partial differential ...
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Higher order Laplacian flows
Given disjoint surfaces $q_i$ in 3D and their 1D boundary curves $\partial q_i = \gamma_i$, I seek a surface $p$ that joins the $q_i$, where $p \cup q_i$ forms a (piecewise) $C^k$ surface that ...
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why DSolve gives different looking solution when using u vs. u[x,t] in the call?
Should the answer by DSolve be different when calling it as DSolve[ode,u,{x,t}] vs. ...
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Mathematica packages for numerically solving the Klein-Gordon and Dirac equations?
The book "Advanced Visual Quantum Mechanics" by Thaller includes Mathematica software packages for the numerical solution of the Klein-Gordon equation and the Dirac equation (subject to user-defined ...
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EventLocator in NDSolve seemingly hogs memory in Windows, but not Mac
I have written a function (ftest in my code) which does the following:
Takes a vector {x,vx,vy} as input
Numerically solves (with high precision) a specific system ...
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Applying method of dominant balance directly to an equation
The non-linear equation $y''(x) = \sin k x y$ for $k\in \mathbb R$ cannot be solved analytically to yield a closed form solution. However, by applying the method of dominant balance one may obtain ...
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Does current Mathematica capability allow solving PDEs (e.g. reaction diffusion equation) over surface of a mesh or surfaces
I came across this nice paper (https://arxiv.org/pdf/1605.01583.pdf) where the authors simulated a reaction diffusion system over the surface of a gecko, primarily to understand how various patterns ...
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System of coupled nonlinear pdes with FEM (magneto-hydrodynamic mass transfer)
EDIT 01
See end of post for an update.
Original Question
I'm trying to reproduce the magneto-hydrodynamic flow studied here using the nonlinear FEM functionality, and have been having trouble ...
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ParametricNDSolveValue causes kernel to crash
Bug introduced in 12.1.1 and persisting through 13.2.0.
In the course of answering question 228693, I found that
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Why Mathematica gives this second solution to this first order linear PDE $w_t+3 t w_x=w$?
This is using V12 on windows 10.
I was trying to verify my hand solution with Mathematica. DSolve gives two solutions instead of one, which I do not understand ...
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Details of NDSolve calling LSODA
Inspired by my question regarding the computation time of NDSolve using the LSODA backend I was wondering how NDSolve is actually calling LSODA (what arguments are sent to LSODA), i.e. what are the ...
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DSolve Returns Incorrect Solutions for First-Order ODE
Bug introduced in 10.4 or earlier and persisting through 11.3. Reported to Wolfram Technical Support as CASE:4150361.
Fifty-one DSolve questions on this site are ...
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Using NDSolve on the Painlevé equations
In an earlier question of mine, I was looking for a way to handle certain kinds of singularities (poles) when using NDSolve. Michael E2's answer, which relied on ...
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Tricky ODE with strange B.C. NDSolve vs. DSolve
This is a tricky ODE. First order.
$$
y'(x)=y^2(x)-2 y(x)+1
$$
This is easily solved by hand, since separable. But the trick is with the boundary conditions. It is $y(1)=1$. When solving it by hand,...
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Alternatives to FiniteElement as Spatial Discretization Method for NDSolve
Finite Element Programming:
[...] It is possible to skip this section and continue with
the discretization stage and make use of the initialized data
structures ...
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Numerically solving system of partial differential equation
I am trying to solve a system of partial differential equation with boundary conditions. But I got an error message saying
NDSolve::icfail: Unable to find ...
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Modify NDSolve`StateData (if possible)
I am trying to solve a PDE that needs to be scaled constantly (refer to this). @andre suggests I modify NDSolve`StateData.
Now, the problem is, I'm not used to ...
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Resolving singularity in convection-diffusion equation using pdetoode
Building on the system of equations in this post, I attempted to solve an additional convection-diffusion equation describing the concentration of solute in the lens, which affects its spreading.
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Spherical harmonics and Laplace operator
The spherical harmonic function $Y_l^m(\theta,\phi)$ is defined to be an eigenfunction of the angular part of the Laplace operator with eigenvalue $-l(l+1)$. In other words, it solves the PDE:
$$\...
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What are the valid options for the "ParametricCaching" option in ParametricNDSolve?
I am using ParametricNDSolve as part of the calculation of an objective function for an optimization, so I am trying to strike a balance between memory usage and ...
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DSolve returns wrong result
I tried to solve a nonlinear, partial differential equation for the function Y[h, x] by using the following code:
...
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Is there a Mathematica CUDA ode solver?
I have a system of ODEs which I'd like to solve with many (thousands) different initial conditions. In the net there are articles that CUDA can speed up such computations, but I haven't found ...
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Incorrect result by DSolve
For real $x$ consider the trivial equation
$$|y'(x)|=-|x|.$$
Since the left side is always positive and the right always negative, there is no solution.
Let's try
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Help implementing Magnus Expansion
The Magnus expansion is a tool to approximate solutions to first-order linear differential equations (the Wikipedia page is quite instructive and concise) - it's particularly useful because all orders ...
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StiffSystem or Singularity - a system of second order ODEs in the problem of geodesics
I would be extremely grateful for any help regarding the following code I wrote and the errors it produces. In this code I am investigating the behaviour of a massive particle trapped in the vicinity ...
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Spectral problem for differential vector operator (calculation of EM field in a cavity)
I know that mathematica has a DEigensystem and NDEigensystem which allow one to find eigenfunction and ...
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Convergence of approximate solutions to obstacle problem for the heat equation
Consider the problem
$$(P) \qquad \begin{cases}
\min\{\partial_t u - \Delta u, u -\varphi \} = 0 & \text{ in } (0,T)\times \mathbb{R}^N \\
u(0,\cdot) = \varphi(0,\cdot) & \text{ in } \mathbb{...
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Change Branch Cut for DifferentialRoot
The differential equation
eqn = (16 + q) g[q] + 4 q (-3 + q^2) g'[q] - 4 q^2 (-1 + q^2) g''[q] == 0
is singular at {-1,0,1}. ...
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what are the limitation on current Mathematica's ability to solving a Sturm-Liouville ODE?
Update
fyi. CASE:3855831 (thanks to bbgodfrey reporting it)
Mathematica 11 is supposed to be able to solve basic S-L ODE according to this page
And it works ...
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APPCRASH of Kernel.exe. running Murphy ODE collection
Since I am getting many KERNEL crashes running Murphy ODE collection, I thought to use this post and collect each crash here instead of making separate post for each one, as there might be too many ...
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1/0 encountured solving Murphy ODE #116
This is another case of DSolve getting 1/0 internally.
Could someone explain why this happens? Is this a bug? does it happen on other platforms? I am using windows 7, 64 bit. This is a non-linear ...
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Solving a system of differential algebraic equations (DAE)
I am trying to solve a system of 8 differential algebraic equations, where equations 3 and 5 are differential equations and the rest are constraints which need to be satisfied. Also I only know the ...
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Naive question on ODE numerical solving and periodic initial conditions
I have a second-order nonlinear ODE for which I would like to find a numerical solution, with periodic initial (boundary) conditions.
Can this be done directly with ...
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NDsolve memory leak
Every time I run NDsolve it uses some memory that I am not able to free later.
The following is an example code based on the spring equation (Hooke's law) that ...
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