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Questions tagged [differential-equations]

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

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

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Example questions:

7567 questions
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Accessing Reduce from DSolve

When solving transcendental equations, Solve frequently warns us that inverse functions are being used so that some solutions may not be found. We also see that Reduce might provide a more complete solution and, indeed, simply changing Solve to…
Mark McClure
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25
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4 answers

Change variables in differential expressions

I have a fairly complicated differential expression in terms of a variable r and two unknown functions of r, B[r] and n[r]. I want to do a Taylor expansion of this around r=infinity. I want to do this by defining a new variable x=1/r and changing…
user1591373
22
votes
1 answer

29 Differential equations hang/not solved in version 11 compared to 10.4, looking for cause

I run Kamke differential equations in version 11 and compared the result to version 10.4. Found 29 differential equations that are no longer solved in version 11. Actually v11 hangs on these, eating more and more RAM with 100% cpu. At least I waited…
Nasser
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2 answers

Solve Laplace equation using NDSolve

I am new to Mathematica, a friend recommended this software and started using it, in fact download the trial version to know. I recently did a program in C to calculate numerically the solution to the Laplace equation in two dimensions for a set of…
Santi Carmesí
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3 answers

Vector form using NDSolve

Michael E2 wrote a wonderful solution for my question. Now I am considering the system: $$ \begin{align*} x'&=x^2 y,\ x(0)=1\\ y'&=-x y^2,\ y(0)=1 \end{align*} $$ I am wondering how I can write this in vector form to produce a solution $\vec r(t)$…
David
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15
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2 answers

How to solve a system of partial differential equations?

Edit: since the upgrade to Mathematica 10, this problem seems solved I just want to solve a system of partial differential equations, for example: $$ \left\{ \begin{array}{l} \frac{\partial}{\partial a}[f(a, b, c)] = 4 \sin^2(b) \cos(c)…
mlpo
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15
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1 answer

Solve a PDE on a domain $\Omega$ with given boundary conditions

I'm starting to study the behavior of some PDEs and I would like to run simulations in mathematica to help me visualize solutions. For example, a prime example that I would like to study is $$ \left\{ \begin{array}{cc} -\Delta\phi +…
nullUser
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14
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3 answers

help to plot Poincaré section for double pendulum

I am reading a book about classical mechanics. In the chapter about chaos, it gives the simplified and scaled equations for double pendulum as $$ \frac{d}{dt}\left[ \begin{matrix} \alpha \\[3mm] l_\alpha \\[3mm] \beta \\[3mm] l_\beta …
user1285419
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14
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1 answer

Why does NDSolve fail to solve the PDEs and spit out mconly warning?

I try to solve two coupled PDEs with NDSolve using the following code: Set two operators: op1[y_, α_, β_] = ((α^2 + β^2)*# - D[#, {y, 2}]) &; op2[y_, α_, β_] = (op1[y, α, β]@ op1[y, α, β]@#) &; Set the parameters: α = 1; β = 0.5; m = 300; Tend =…
lxy
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1 answer

How to use NDSolve with moving boundary conditions?

So I am trying to solve the movement in space and time of a spreading gravity current. The interface satisfies the following PDE: $ \frac{\partial h}{\partial t} = \frac{\partial}{\partial x}\left(h^3 \frac{\partial h}{\partial x}\right) $. The…
mch56
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13
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1 answer

NDSolve Differential Equation Error

I am trying to solve the following differential equation- k = NDSolve[{y'''[x] == -76*Sin[y[x]], y[0] == Pi/4, y'[0] == 0, y[1.85] == 0}, y, {x, 0, 2}, AccuracyGoal -> 10, PrecisionGoal -> 30] I am getting a solution but when I plot a graph,…
valmiki
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13
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1 answer

Solving the mean field Kuramoto model with NDSolve

I would like to numerically solve a system of differential equations that describes the dynamics of $N$ coupled oscillatory units (Kuramoto model) via their phase variables $\phi_i$: $\frac{\partial\phi_i}{\partial t} = \omega_i +…
Oscillon
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2 answers

DSolve misses a solution of a differential equation

[Note that in the cited duplicate, DSolve not finding solution I expected, the general solution returned by DSolve is missing a solution for quite different reasons than this one. In the duplicate question, the missing solution may be obtained as…
Ferenc Beleznay
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11
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2 answers

Solve a nonlinear PDE equation with a Neumann boundary condition

I am trying to use Mathematica 10 to solve a PDE $$u_t=u_{xx}+u_{yy}+u(1-u),$$ in the unit disk $(x,y) \in D=\{(x,y):x^2+y^2<1\}$, with the Neumann boundary condtion $$\frac{\partial u}{\partial n} \bigg|_{\partial D}=0,$$ and the initial…
xpaul
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10
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3 answers

Wrong answer from DSolve?

I was trying to solve the initial value problem $$u'(t) = \sqrt{u(t)} + \frac{1}{n+1}, \, u(0) = 0$$ using DSolve: DSolve[{u'[t] == Sqrt[u[t]] + 1/(n + 1), u[0] == 0}, u, t] The output for this command in Mathematica 9 is: {{u -> Function[{t}, …
shamisen
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