Questions tagged [differential-equations]

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

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Solve a Differential equation analytically instead of numerically

I want to solve the differential equations (shown below in the list 'eqs') analytically instead of numerical. Using NDSolve the following code works perfectly fine but using DSolve it doensn't. I ...
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1answer
107 views

Vector ParametricNDSolve and FindRoot interaction

This question came out of this question. I have a set of differential equations, written in vector form. I'm only interested in the value of these at the endpoint, and so I use ...
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38 views

Why DSolve gives the error “Arguments should be ordered consistently” on this PDE?

This problem is strange. Mathematica is able to solve this PDE with no error ...
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2answers
2k views

Turing patterns

I am new in learning Turing patterns. Is there any sample code available to generate such patterns in ecology model (Lotka–Volterra model)? The above figure is taken from this paper, and is based on ...
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3answers
483 views

How to set interface conditions for optical waveguide in NDEigensystem?

I have been working on waveguide mode analysis using FEM in Mathematica for a week, but I haven't succeeded until now. The optical fiber-like waveguide is featured with different refractive index in ...
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1answer
72 views
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1answer
49 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 ...
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2answers
115 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. ...
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2answers
85 views

Vector-valued ParametricNDSolve, solving for a combination

I am integrating two vector differential equations using ParametricNDSolve, one for $\mathbf{Y}$ and one for $\mathbf{Z}$, and then I'm interested in a combination ...
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1answer
64 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 ...
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0answers
56 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 ...
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2answers
156 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
74 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 ...
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2answers
53 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, ...
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1answer
51 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, ...
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4answers
81 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 ...
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0answers
77 views

Mathematica running out of RAM while executing NDSolve

I am playing with Mathematica to solve the 2D-wave equation with the code below: ...
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2answers
437 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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39 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. ...
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2answers
660 views

How to plot an unstable attractor?

I'm trying to solve and plot the following in Mathematica: ...
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2answers
282 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
175 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
50 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
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 ...
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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 $T(t,\partial_t)$. ...
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0answers
41 views

ParametricNDSolve many functions and plotting

I don't understand why I don't get the plots : ...
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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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1answer
43 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
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 ...
9
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3answers
248 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 ...
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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

Fitting 2 curves nonlinearmodelfit

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1answer
57 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 ...
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1answer
63 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
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 ...
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 ...
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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}[...
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1answer
65 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
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 $k(t)$: <...
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1answer
90 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 ...
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1answer
47 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 ...
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1answer
77 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 ...
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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
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1answer
50 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 ...
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1answer
59 views

Stiffness and NDSolve error NDSolve::ndsz:

I have a 2nd Order ODE problem I am trying to solve numerically in Wolfram: $$ (k^2-1+\frac{2x}{x^2+c^2})\frac{d^2y}{dx^2}+\frac{c^2-x^2}{c^2+x^2}\frac{dy}{dx}+x\frac{x^2-3c^2}{(x^2+c^2)^3}y=0 $$ ...
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1answer
55 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
39 views

WhenEvent versus If function for ODEs

The following equation works for ParametricNDSolve ...
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1answer
51 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
107 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 ...