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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0answers
63 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 ...
6
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2answers
194 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 ...
2
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1answer
81 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 ...
2
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2answers
62 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, ...
1
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1answer
54 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
92 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 ...
2
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0answers
87 views

Mathematica running out of RAM while executing NDSolve

I am playing with Mathematica to solve the 2D-wave equation with the code below: ...
4
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2answers
443 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. ...
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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. ...
6
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2answers
665 views

How to plot an unstable attractor?

I'm trying to solve and plot the following in Mathematica: ...
4
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2answers
326 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
199 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. ...
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1answer
54 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: ...
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1answer
46 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
36 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 $T(t,\partial_t)$. ...
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0answers
50 views

ParametricNDSolve many functions and plotting

I don't understand why I don't get the plots : ...
1
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0answers
60 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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1answer
55 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( ...
0
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0answers
94 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 ...
9
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3answers
304 views

Stress analysis in axisymmetric bodies

I would like to do some finite element calculations in axisymmetric cylindrical coordinates. I wish to calculate stress in terms of {r,z} coordinates. The radial ...
0
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0answers
51 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

Fitting 2 curves nonlinearmodelfit

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0answers
32 views
5
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1answer
69 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 ...
-1
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1answer
75 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
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1answer
80 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 ...
2
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1answer
60 views

DSolve Doesn't Return a Solution or Error

DSolve is not returning anything other than the original expression on ...
0
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0answers
45 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
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1answer
72 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. ...
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0answers
60 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
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1answer
101 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
56 views

Could not able to set up a differential equations using EulerEquations command

I have a constructed the Lagrangian of a mechanical system by finding the kinetic and potential energy of the system. Then I tried using EulerEquations to set up a differential equation by taking the ...
0
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1answer
99 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 ...
0
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0answers
32 views

DSolve not giving a solution

I tried solving this but no result, I tried eliminating the initial condition, replace the zeroes in boundary condition but nothing is working. Thank you in advance
0
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1answer
53 views

How to keep the numerical integration when an event occurs?

I'm numerically integrating the following system, f[r_] = 0.904965 - (1 + 12.7028/r^2) (1 - 2/r) dϕdλ = 1/r[λ]^2; eqc = r'[λ] == Sqrt[f[r[λ]]/(dϕdλ^2)]; with the ...
1
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1answer
66 views

Stiffness and NDSolve error NDSolve::ndsz:

I have a 2nd Order ODE problem I am trying to solve numerically in Wolfram: $$ (k^2-1+\frac{2x}{x^2+c^2})\frac{d^2y}{dx^2}+\frac{c^2-x^2}{c^2+x^2}\frac{dy}{dx}+x\frac{x^2-3c^2}{(x^2+c^2)^3}y=0 $$ ...
0
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1answer
68 views

Solve Heat Equation with Source Term and Neumann BC

I am trying to find a solution on mathematica to $ \partial_tu-\partial_{xx}u= \cos(2\pi x), \; 0<x<1,\; t>0 $ $ \partial_xu(0,t)=\partial_xu(1,t)=0, \; t>0 $ $ u(x,0) = \...
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0answers
40 views

WhenEvent versus If function for ODEs

The following equation works for ParametricNDSolve ...
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 ...
3
votes
2answers
113 views

How do I solve a certain differential equation?

I need to find out a solution to the equation: z r[z] r''[z] - (d - 1) r[z] (r'[z])^3 - (d-2) z (r'[z])^2 - (d - 1) r[z] r'[z] - (d - 2) z == 0 subject to the ...
0
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0answers
54 views

Problem with NDSolve and Manipulate function

I'm having an issue with commands NDSolve and Manipulate. I'm trying to represent the rotation spin, nutation and precession of a spinning top (approximated to an inverted cone). Under specific data ...
1
vote
2answers
112 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: ...
2
votes
1answer
89 views

ParametricFunction from ParametricNDSolveValue changes when evaluated?

I am new to using ParametricNDSolveValue (and ParametricFunctions in general), so I am hoping that I have made a simple error. First I set up a system of differential equations: ...
1
vote
1answer
45 views

How to provide a system of input every x time interval (e.g, x=1 week)

The following code described an input to the system only during t less than minInfusionTime after time zero. Any way to give this same input every x time (e.g. every week) after time of zero, to an ...
0
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1answer
64 views

DSolve not working on vector equation

Ok, so I'm trying to solve a differential equation of motion, and mathematica doesn't do anything to my input. It just leaves it unevaluated. I know that the system is physically solvable with not ...
4
votes
2answers
143 views

Non Linear Model Fit - Fitting ODE to Data

Thank you everyone for your meaningful contributions! My Goal and Problem I'm trying to fit a particular ODE in a set of ODE's to experimental data. I've attempted to implement this by following the ...
0
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2answers
65 views

Parametric Find Maximum

I'd like to plot the maximum of a curve in function of a parameter. Meaning I looking for maxima that depend on a parameter. Here is what I tried to do but FindMaximum is not parametric, so it did ...
1
vote
1answer
33 views

FindMaximum with parametrized NDSolve

I am trying to solve a parametrized ODE, and wanting to find the parameter that maximize the solution at a specific point. For example, in the following code I am trying to solve the ODE $df/dz=t \...
1
vote
3answers
141 views

Why doesn't Mathematica evaluate the series with recursion relationship as expected?

I define a series $dg(i)$ as the $i$th derivative of a function $g[t]$ for $i>0$ and known the first term $dg(1)=(t-x)g(t)$. In mathematica, the code is: ...
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: ...