Questions tagged [differential-equations]

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

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2
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1answer
166 views

How to solve a PDE with periodic boundary conditions in one of the variables?

I need to solve a PDE where one of the variables is an angle, so I need to know how to deal with periodic boundary conditions. As a warm up, I am trying to solve the Helmholtz equation in polar ...
0
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2answers
117 views

Mathematica unable to interpret equations in DSolve

I'm trying to solve a system of seven ODEs with seven conditions. Since the following approach using DSolve is yielding the same output as the input, Mathematica can't find a solution. ...
1
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1answer
51 views

Using ParametricNDSolve to solve a hysteretic ODE (Wolfram Mathematica 10.0)

I am trying to solve an ordinary differential equation using ParametricNDSolve and I want to fit the solution to some data to get the value of the parameter. The problem I have is that the ODE is ...
5
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2answers
164 views

Solving linear coupled PDEs by FDM

I am trying to solve some linear, coupled PDEs for perturbative analysis (first order in time, 3rd order in space), for which I then plan to take the global spatial maxima of their magnitudes and plot ...
0
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0answers
92 views

Simplify the equation in terms of function and coefficients?

I have two fourth order differential equations and eight boundary conditions. I want to get my result in terms of function (Y) and coefficients (let say P1, P2 and so on). I used Dsolve to get the ...
3
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1answer
68 views

Hat function(UnitTriangle[x]) is really applicable in Finite Element Method?

I am learning finite element method(galerkin method) for solving ode/pde. when searching this topic, I often see examples using the hat functionUnitTriangle[x] as ...
2
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0answers
57 views

Formulating equations for 3D stress in the finite element method

I would like to know how you formulate equations for the finite element method for stress calculations. We know the answer because user21 has put it here. It involves usage of ...
5
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1answer
126 views

Analyzing MethodOfLines

In this example the wave equation ...
2
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1answer
78 views

NDSolve cannot evolve Gaussian wave packet with small width

I want to solve a 1d wave equation with initial conditions: $$ u(x,0) = f(x) = e^{-(x - x0)^2/2\sigma^2} \ \ \text{and}\\ u_t(x,0) = - f_x(x) $$ The second condition is the advection equation and ...
8
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2answers
704 views

2D inhomogeneous biharmonic equation

How to solve a 2D inhomogeneous biharmonic equation with NDSolve? I tried the following code: ...
33
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4answers
3k views

Dynamic Euler–Bernoulli beam equation

I am trying to solve for the vibration of a Euler–Bernoulli beam. The equation is $\frac{\partial ^2u(t,x)}{\partial t^2}+\frac{\partial ^4u(t,x)}{\partial x^4}=0$ For the boundary conditions I ...
2
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2answers
54 views

WhenEvent ignores some actions

I've got a problem where WhenEvent successfully detects an event, but then performs only some of the actions. In this minimal example, ...
0
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1answer
75 views

NDSolve gives unexpected results when using the method of lines

I've been trying to solve the following PDE using the NDSolve function but it seems something is not working properly. The PDE is a the heat equation on polar coordinates and assuming angular simmetry:...
1
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1answer
52 views

Area of a parametric plot with interpolating functions

I am looking for the area of a parametric plot defined by two solutions (defined as: VVLt & PVLt) of Numerically solved differential equations. The problem is when i'm trying to integrate the two, ...
1
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4answers
82 views

How to put solutions of mutiple DEs with NDSolve in table

I have $N$ differential equation for each $s \in {1,2,...,N}$ on the domain $x \in [1,2]$ of the form (e.g.) $xf_s'(x) + \log(xs) f_s(x)+1 = 0$, with the boundary condition $f_s(1) = e^{-s}$ Now I ...
1
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1answer
395 views

PDE raises NDSolve::ntdvdae, then kernel quits

In a related question, the SolveDelayed->True option seemed to solve the problem. SolveDelayed is not a valid option in M10 (...
2
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1answer
89 views

Output of intermediate results from very long NDSolve computation into sequenced CSV files

There is a problem that I was not able to solve for months, if not years, and I can't postpone it any longer. It is this: I know how to output the result of a computation from NDSolve into a file ...
4
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2answers
305 views

Nonlinear boundary value problem of ODE involving principal value of integral

I have asked a question on a nonlinear eigenvalue problem (EVP). And I have worked on these for a week but I cannot solve it. I think I should first try to solve the related ODE boundary value problem ...
8
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1answer
183 views

Fitting multiple data with model and NDSolve with different initial conditions, and other shared parameters

I know that there are already questions about fitting multiple datasets and about NDSolve and about shared and non shared parameters, but I tried to apply them and some things are still not clear. ...
4
votes
2answers
439 views

Plot exactly N bounce of a ball

I want to plot exactly N bounce of a ball. I'm using DSolve to solve the differential equation and WhenEvent to change the velocity. The code below plots only the first 10 seconds. ...
0
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0answers
40 views

NDSolve: evolutionary singularity in coupled differential equations

I am trying to solve coupled differential equation where a function attains a value such that its derivative is infinite. ...
1
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0answers
58 views

Specify direction of propagation in the 1-d wave equation in NSolve and NDSolve [duplicate]

I am solving the 1-d wave equation with the following initial conditions: ...
2
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0answers
84 views

Mathematica running out of RAM while executing NDSolve

I am playing with Mathematica to solve the 2D-wave equation with the code below: ...
15
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2answers
727 views

What boundary is added when boundary condition is not sufficient?

When insufficient boundary conditions are given to NDSolve for solving PDE, usually the warning NDSolve::bcart pops up: ...
6
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2answers
660 views

How to plot an unstable attractor?

I'm trying to solve and plot the following in Mathematica: ...
0
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1answer
39 views

Unable to get the expression of solution in DSolve

I am trying to solve the 1D Diffusion equation for a sigmoidal function. However I cannot the expression of the solution ...
0
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1answer
51 views

Fitting system of differential rate equations to data

I am trying to fit a set of differential equations to experimental data, without luck so far. These are the data: ...
5
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1answer
59 views

How to change the default normalization for NDEigensystem?

I'm currently using NDEigensystem to solve a PDE that describes a particle travelling on a hyperbolic (negatively curved) surface. However, the eigenfunctions that are returned by NDEigensystem are ...
0
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1answer
42 views

Evaluation Control for Equation Input to NDSolve

I am trying to numerically integrate a system of equations using NDSolve and am having issues with symbolic matrix inversion taking a long time. The actual system is much more complicated, but I have ...
0
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1answer
35 views

Calculation of evolution equation with NDSolve

I have near to no experience with mathematica, so this might seem pretty trivial. I want to solve an Evolution equation, i.e. we have a function $f(t,x)$ and a differential operator $T(t,\partial_t)$. ...
0
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0answers
45 views

ParametricNDSolve many functions and plotting

I don't understand why I don't get the plots : ...
0
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1answer
47 views

Delayed differential equation with convolution

So I have a differential equation : $\left\{\begin{split} & c'(t) = \alpha q(t) c(t)^{2/3} - \beta(1 - q(t))c(t)\\ &\chi'(t) = \kappa c(t) q(t) \\ & q(t) = \int_{-\infty}^t \Big( ...
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0answers
45 views

NDSove vs ParametricNDSolve

ParametricNDSolve is very practical when one has to execute NDSolve again and again. However is it equally accurate? I have not ...
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0answers
50 views

Problems with parameters

I want to plot an ellipsoid and geodesic on it depending on a, b, c. What is wrong with my code? I mean there is problem with Manipulate, if I remove this command and parameters a, b, c, then ...
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0answers
27 views
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0answers
29 views
2
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1answer
59 views

DSolve Doesn't Return a Solution or Error

DSolve is not returning anything other than the original expression on ...
4
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1answer
181 views

Neumann boundary condition is not satisfied

I want to solve the diffusion equation on a disk centered at (0,0) with a radius of 1. I also want the flux at a radius of 0.8 to be zero. I have this initial condition at time zero: ...
-1
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1answer
64 views

Laplace equation for cylindrical rods

I have a system of four cylindrical rods with a certain radius, length, and separation. I have applied different voltages to the rods. I want to solve the Laplace equation, but I am unable to give ...
4
votes
1answer
73 views

Why unable to verify solution to first order PDE?

This is using V12 on windows. I solved this PDE by hand and wanted to ask Mathematica to verify my solution. But Mathematica solution does not look like mine. And when I tried to verify Mathematica ...
10
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2answers
362 views

Solving a wave equation over the Black Sea shaped region

There is a code for solving a wave equation over an arbitrarily shaped region. ...
0
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0answers
36 views

How to solve integral equation involving Fourier Series

I have a set of equations involving two anti periodic functions $f(t+T)=-f(t)$ and $g(t+T)=-g(t)$ \begin{cases} f(t)&=J^2g(t)^3 \\ \mathcal{F}[g](\omega_n)&=\frac{1}{-i\omega_n-\mathcal{F}[...
3
votes
1answer
66 views

How to increase the integration domain of NDEigensystem without a “non-Hermitian” error?

Recently, I've been using NDEigensystem to solve a two-dimensional eigenfunction equation. The region that I'm solving over is as follows. ...
1
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2answers
103 views

Fitting experimental data with a parametric function

How does one use a fitting routine such as NonlinearModelFit with a ParametricFunction? Example below: First let's generate some data: ...
0
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0answers
55 views

Take limit in NDSolve

I have this equation : eqkk = D[k[t], {t,2}] - ((3 sola'[t]/sola[t]) + (3 sola''[t]/sola'[t]) - (1/(sola'[t] sola[t]^2))) D[k[t], t] To get $k(t)$: <...
2
votes
1answer
92 views

Poincaré sections for oscillating system

I need to build Poincare maps for solutions of a system of differential equations. This system includes the mass of an oscillating particle. If the mass value is made very small (m ~ 10 ^ -25) the ...
0
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1answer
82 views

Using multiple boundary conditions with NDEigensystem

I'm quite new to Mathematica and to Stack Exchange so I apologise if this question has already been answered. I've recently been trying to solve a partial differential equation to find the ...
20
votes
4answers
849 views

What is the definition of Curl in Mathematica?

I have a usual mathematical background in vector and tensor calculus. I was trying to use the differential operators of Mathematica, namely Grad, ...
1
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1answer
108 views

How to fit my data to an ode

Here is system of ODEs and data, where I am trying to use the real data to estimate some governing parameters. ...
1
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1answer
52 views

DSolve behaves weirdly with dynamic [duplicate]

I am an beginner in using dynamics as well as mathematica. I am trying to ask mathematica to solve and plot the solution of X'=AX with dynamic every time my matrix A updates. However the Dsolve ...