Questions tagged [differential-equations]

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

962 questions with no upvoted or accepted answers
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12
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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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964 views

From where to learn finite element method?

Can anyone reccomend me a book or site for learning finite element method with mathematica, besides wolfram language official site, https://reference.wolfram.com/language/FEMDocumentation/tutorial/...
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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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309 views

DSolve breaks when the ordering of independent variables aren't proper?

Bug introduced in 3.0 or earlier and persisting through 12.0. I encountered this when trying to solve this problem with DSolve: ...
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4k views

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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117 views

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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113 views

What does DSolve`DsolveLaplaceTransformDump` mean in solution of DSolve?

Reported to Wolfram with CASE number 4028951 on 11.3, ...
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382 views

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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557 views

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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297 views

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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520 views

How to put 2 or 3 NeumannValue conditions?

I want to solve numerically the heat exchange of a fin in transient state and two-dimentional, here is my attempt but instead of put DirichletCondition on ...
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2k views

Using NDSolve for Integro-Differential Equations

I have a fairly complicated set of coupled non-linear integro-differential equations that I am trying to solve using NDSolve. The equations are: $\dot{x}=\big|y(t)-x(t)\big|^{1/n}\left[\text{Sign}[y(...
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63 views

What's the solver behind Method -> {“EquationSimplification” -> “MassMatrix”}

Related: What's behind Method -> {“EquationSimplification” -> “Residual”} By reading the document carefully, I've learnt that there are 3 possible options in "EquationSimplification" for DAE systems: ...
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97 views

DSolve fails with four variables

How is that DSolve has no trouble solving this: DSolve[{ D[G[x1,x2,x3],x1]==0, D[G[x1,x2,x3],x2]==0, D[G[x1,x2,x3],x3]==0 },G[x1,x2,x3],{x1,x2,x3}] but it fails ...
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115 views

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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306 views

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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78 views

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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508 views

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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103 views

Order of boundary condition inside DSolve matters?

Bug introduced in 11.1.1 or earlier. Consider the following example: ...
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508 views

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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75 views

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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310 views

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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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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78 views

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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116 views

Where is 1/0 coming from in this call to DSolve?

Bug introduced in 11.3 or earlier and persisting through 12.0 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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80 views

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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209 views

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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202 views

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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119 views

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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177 views

Spurious DSolve Solution

Bug introduced in 8.0.4 or earlier, persisting through 12.0. DSolve quickly returns solutions to the following PDE (which is the homogeneous portion of the PDE in ...
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2k views

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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134 views

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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160 views

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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287 views

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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467 views

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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294 views

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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172 views

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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134 views

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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777 views

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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167 views

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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116 views

unhandled win32 exception in WolframKernel.exe in DSolve of non-linear ODE in one variable

Bug persisting through 10.4. (windows 7, 64 bit) Installed 10.3.1 and started to run some old ode's. in V 9, this ode used to return unsolved, which is ok, but in 10.3.1 now the kernel crashes. This ...
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170 views

Error with DSolve

I am trying to solve the following partial differential equation for the function $f(x,y,z)$ $\frac{(\alpha -\beta y)}{1-y^2}\left(\frac{\partial f}{\partial x} + \frac{(\alpha y-\beta ) }{\sqrt{1-...
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824 views

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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520 views

NDSolve PDE, not enough boundary condition?

The PDE that I want to solve is: $$ \frac{\partial f}{\partial t} + \frac{1}{m} \left( p_x \frac{\partial f}{\partial x} + p_y \frac{\partial f}{\partial y} + p_z \frac{\partial f}{\partial z} \right) ...
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778 views

Numerically solving a system of PDEs where one function is composed with the other

I'm trying to solve the following system using NDSolve: $$ \begin{align} u_t(x,t) &= u_{xx}(x,t) - v(x,t) \\ v_t(x,t) &= u(v(x,t),t) \end{align} $$ with $...
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4k views

NDSolve: methods and step size choosing

I am looking into the documentation of NDSolve[]; more precisely how this function chooses the StepSize and how it chooses which ...
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70 views

Strange behavior of WhenEvent, a bug?

I really feel sorry that I have asked too many questions on this forum about DAE. But I'm indeed facing a lot of problems on this topic and NDSolve. Once again I ...
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42 views

NDSolve`ProcessEquations inside Manipulate

NDSolve and NDSolve`ProcessEquations can handle equations with vectors on each side like this one: ...
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133 views

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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