# Questions tagged [differential-equations]

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

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### 1D-waveequation with absorbing boundary condition: FEM solution?

I try to simulate the special absorbing(?) boundary condition Derivative[1, 0][y][1, t] + Derivative[0, 1 ][y][1, t] == 0 which only allows energy flow in ...
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### Exclude a term in a differential equation

How can I exclude this term (The red box) from derivation to make it consider it as a constant (Just a constant to be multiplied ), I am getting the differentiation for the whole equation but I want a ...
95 views

### Avoiding instability and missing boundary condition errors when solving a system of 3 differential equations

I am trying to solve this system of equations: dw(v,t)/dt =2g(v,t) w(t,v) g(t,v)= Pi/2 (v^2)d g0(v,t)/dt d go(v,t)/dt + d/dv[dw/dt *1/v^3)]=0 with initial ...
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### Functions can graph but can't solve for partial derivatives

First I got a function g[xo,yo] by solving a system of partial differential equations ...
100 views

### Solving boundary value problem with coupled odes at interface

I am trying to get the eigenvalues of the following differential system ...
226 views

### 3D stable fluids algorithm to simulate transition from laminar to turbulent flow

This algorithm is 3D extension of our 2D algorithm published on this page and here. We suppose that with this code we can simulate transition from laminar to turbulent flow. In this example we compute ...
518 views

### Numerical solutions of active 1D wave equations

I would like to solve the following PDE with finite difference method. The PDE is from the following paper, (https://arxiv.org/pdf/1911.11823.pdf). I would like to implement the algorithm for the left ...
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### Draw phase portrait with StreamPlot on a sphere [closed]

I would like to draw this phase portrait using StreamPlot on sphere as in this picture like that In fact, i have seen this for the classical pendulum defined by ...
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### NDSolve solutions for modeling convection-coupled melting

I am trying to solve the convection-coupled melting benchmark in MMA 12.3 as presented in FEniCS/03-ConvectionCoupledMelting-MixedElement-AMR.ipynb. This model in MMA is based on the solution from ...
91 views

### On the quotation mark around Method option in NDSolve

I note that in the documents about NDSolve or its variants, the main Method option has no quotation mark while its sub-...
81 views

### Plotting NDSolve solutions for an ODE with a variable parameter

Quick question! I'm supposed to plot solution curves for the ODE y'(t)+nty(t) = 0, y(0) = 3 with integer n varying from 1 to 6 inclusive. In the process, I have to use interpolated functions obtained ...
136 views

### Normalizing singularities in NDSolve

I've tried to create the following example. Suppose that I have the differential equation: $$U''(x) = \frac{U'(x) - U(x)}{x},$$ which I know 1 boundary condition and know that this function should ...
188 views

### 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(...
288 views

### Solving a Cauchy problem related to the pendulum

One end of a thread of length l = 1m is fixed, and a body of m = 1 kg is attached to the other end. The body is displaced counterclockwise by 30 degrees and then released. Plot the resulting Phi(t) ...
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### Mathematica 12.0 Dsolve solving 2D diffusion PDE

my friends,i meet some problems,please help me! this is my equation and ic ,bc this is my code .I let some constants R,in,D,F become 1，h become 2，it is convenient to calculate ...
159 views

### Stability analysis of coupled ODE's

I'd like to reproduce Panel A of Figure 7 (red curve) of this paper, which represents the steady-state solutions of four coupled ODE's, and verify this claim that the diagonal branch in the Z-shape ...
63 views

### Plot with Dsolve

I am trying to plot the solution to the Dolve at a position /. x -> 0 ...