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

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1
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1answer
32 views

Error with using NDSolve

I am currently trying to numerically solve a system of differential equations. Here is my code: ...
0
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0answers
24 views

Solving coupled differential equations with an eigenvalue

I have 2 coupled differential equations with an eigenvalue Ei and want to solve them ...
0
votes
2answers
34 views

Create a random 2x2 matrix with a repeated eigenvalue and single eigenvecor

Does anyone have a good technique for creating a random $2\times 2$ matrix that has one eigenvalue of multiplicity two, but only a single eigenvector? And more generally, has anyone written a ...
0
votes
1answer
98 views

Time evolution of a wave packet from the time-independent Schroedinger equation [duplicate]

Starting off with the time-independent Schroedinger equation (TISE) $\quad \quad -\frac{\hbar^2}{2m} \nabla^2 \psi + V(r, \theta) \psi = E\, \psi,$ I would like to study the time evolution of an ...
0
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1answer
30 views

Creating a stream plot of nonliner diff equations [on hold]

How would I create a stream plot (of eccentric closed curves) out of the following two equations ...
0
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0answers
25 views

Why does the following NDSolve command not work [on hold]

I am trying to use the following NDSolve command however it does not work and I do not know why. The command is ...
0
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1answer
41 views

NDSolveValue with Map

I have: ...
0
votes
1answer
64 views

Plotting a NDSolve solution

I'm working on a neutrino oscillations problem, and am running into issues ploting the solution to my differential equations. The equations have non-analytic solutions so I'm using the ...
4
votes
1answer
96 views

NDSolve to solve a PDF

I would like to solve numerically the following PDE: $$ \frac{\partial}{\partial t} p(x,t)=-\frac{\partial}{\partial x}p(x,t)+\frac{1}{2}\frac{\partial^2}{\partial x^2}[x^2\,p(x,t)],\;x\ge0,\;t\ge0, ...
0
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0answers
36 views

Integro differential eq boundary difficulties

I'm trying numericaly solve simple integro-differential equation, but have some problems with boundary conditions. System: ...
-3
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1answer
55 views
0
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2answers
42 views

Problems solving/plotting a differential equation

I am trying the following: Plot[DSolve[{1220*x''[t] + 1000*x'[t] + 35600 x[t] + 4500*x[t]^3 + 2135 == 0, x[0] == 0, x'[0] == -5}, x, t], {t, 0, 10}] Could ...
5
votes
1answer
71 views

Detecting nearly simultaneous WhenEvents in NDSolve

I am trying to solve a system of (many) coupled nonlinear ODEs. I need to decouple some of the equations (i.e. set the time derivatives of some of the dependent variables to zero) at various points in ...
0
votes
1answer
78 views

How to adjust excel data for NonlinearModelFit?

I'm really new to Mathematica and I'm facing a problem and would really appreciate some help! Maybe my question is similar to one described in How to fit 3 data sets to a model of 4 differential ...
1
vote
3answers
146 views

Solving differential equation

I want to solve the following differential equation DSolve[y''[x] == (λ y[x])/Sqrt[-1 + x], y[x],x] But do not know how to actually solve it. Any suggestion?
0
votes
1answer
66 views

NDSolve::bcedge: Boundary condition not specified on a single edge

NDSolve::bcedge: Boundary condition c[t,5]==Cout is not specified on a single edge of the boundary of the computational domain. >> I'd like to plot $\frac{\partial}{\partial ...
0
votes
0answers
62 views

DSolve response with DSolve

I'm trying this code ...
1
vote
1answer
85 views

Solving ODES in order to find unknown constants

I am trying to solve a set of ODES which represent a second order consecutive chemical reaction. ...
0
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0answers
30 views

How to sweep a parameter in an ODEs system using ParametricNDSolveValue?

I want to analyze how my ODEs system behaves when I change only one parameter (in this case d). ...
0
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0answers
41 views

Solving a big System of ODEs

I want to solve numerically a linear first-order ODE system with over 12000 equations. I used NDSolve with implicit options: ...
0
votes
1answer
70 views

NDSolve solving problem

I am trying to solve for the function y[x] obeying the ODE: $ \frac{x}{1 + x}y^{\prime\prime}(x) + \frac{2 x + 1}{(1 + x)^2} y^{\prime}(x) = \frac{1}{3\sqrt{y(x)}} ...
2
votes
2answers
170 views

Solve ODE in State-space form

Is it possible to solve an ODE in state-space form in mathematica? Such as x'[t]=A.x[t] I attempted ...
1
vote
1answer
104 views

Forcing solutions to avoid Root[]

I'm solving a system of ordinary non-homogeneous differential equations (4 equations). The solutions will include some algebraic equations solutions as known from text books due to the use of an eigen ...
2
votes
2answers
156 views

Exact Differentials

I just started using Mathematica so my apologies if this is a very basic question. I tried to find related questions on this forum but couldn't, so here goes. I have an equation, $\quad \quad dp ...
4
votes
3answers
315 views

Verify Cayley-Hamilton Theorem

Consider the matrix: A = {{-1, -4, -2}, {0, 1, 1}, {-6, -12, 2}} Now, the characteristic polynomial is found: ...
0
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0answers
43 views

How to plot three related differential equations in Mathematica?

Eq1: $ \frac{1}{3\phi}=\left[\frac{x}{x+1}\frac{d^{2}}{dx^{2}}+\frac{2x+1}{(x+1)^{2}}\frac{d}{dx}\right]{\phi^{2}} $ Eq2: $ ...
0
votes
1answer
121 views

How can I create a phase plane? [duplicate]

I want to make a phase plane for an equation system. I want it to look something like a Mu-Space in Stat-Mech. Basically I want it to show the same system with various different initial condition ...
1
vote
4answers
136 views

How can I remove horizontal lines on a phase plot for a pendulum?

I am attempting to do a phase plot for a driven,damped pendulum. When the angle wraps from Pi to -Pi or -Pi to Pi I get a horizontal line on the plot. I would like to remove these lines as they mask ...
0
votes
0answers
48 views

find initial condition for NDSolve

I have a complicate second order differential equation to solve numerically (too complicate to be posted). Unfortunately I do not know the behavior of the solution $\theta(r)$ near $r=0$ and I am not ...
1
vote
1answer
100 views

Poisson PDE in a rectangular domain

I found a solution for this problem, but this is in Scilab and I never use Scilab. Can anyone can help me to translate it in Mathematica? Here is the Link:http://imechanica.org/files/TorqueR.pdf I ...
0
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0answers
38 views

Trying to plot solution curves on top of a direction field

I'm trying to do some diff. eq. homework that requires taking a general solution to a differential equation and graphing a series of possible solution curves over a direction field of the general ...
4
votes
2answers
109 views

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 ...
1
vote
0answers
55 views

NDSolve Poisson PDE for rectangle with hole

When I solved the Poisson PDE with function NDSolve in a rectangular domain with hole in the center, and search the first derivative with x and y why appear these protrusions on the diagram around the ...
0
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0answers
97 views

Laplace PDE in a polar coordinate system

I want to solve a Laplace PDE in a polar coordinate system with finite difference method, but I have a problem with boundary conditions at r = 0. Here is what I ...
2
votes
1answer
61 views

NDSolve for axisymmetric problem

I would like to solve an axisymmetric Poisson equation on a disk with FEM. The code for Cartesian coordinates works fine: ...
3
votes
1answer
87 views

Define and refine mesh around a hole

I am solving Laplace equation with particular geometry and boundary conditions: ...
1
vote
0answers
36 views

Error message for FEMStiffnessElements

I am trying to solve this pde numerically with Mathematica: ...
2
votes
2answers
79 views
2
votes
2answers
127 views

Fighting the Current

I am working a problem I am working on. A boat start across a river at the point (c,0) and points its bow directly across the river to the point (0,0). The parameter a is the river current velocity, b ...
2
votes
0answers
33 views

How to handle solution returned by ParametricNDSolveValue in FindRoot

i was trying to solve a problem relative to root finding in a system of differential equations; here's a simpler case. With two distinct set of parametric differential equations, i'm able to find the ...
1
vote
1answer
74 views

DSolve for a huge linear inhomogeneous ODE in parallel

I have a linear inhomogeneous ODE with constant coefficients, which I need to solve symbolically. The problem is that the inhomogeneity is sum of more than 100 terms (however, each term itself is ...
1
vote
1answer
114 views

4th-order Runge-Kutta method to solve a system of coupled ODEs [duplicate]

I am a beginner at Mathematica programming and with the Runge-Kutta method as well. I'm trying to solve a system of coupled ODEs using a 4th-order Runge-Kutta method for my project work. I have ...
3
votes
2answers
66 views

Memory Problem with Modules and NDSolve

I'm using NDSolve inside a module, and I appear to have a memory leak. The relevant code is: ...
3
votes
2answers
151 views

NDSolve in Mathematica won't use all the cores avaiable

When I solve a system of differential equations in Matlab, the task manager shows that all the CPU cores are in use. This is not true when I solve the same system in Mathematica. I have six cores. ...
1
vote
1answer
75 views

How to modify a PDE inside NDSolve according to an if condition

I need to solve this PDE $$\partial_tf(t,x)+\partial_xf(t,x)+k\partial_{xx}f(t,x)-xf(t,x)=0 $$ with $k\in\mathbb{R}$ and final condition $f(T,x)=1$ with $0<t<T$. My problem is how to solve ...
0
votes
2answers
99 views

Solving differential equations with Wolfram Mathematica

So i saw this differential equations in my textbook $\frac{{{d^4}\omega }}{{d{x^4}}} + 4{\lambda ^4}\omega = 0$ and i figured why not solve it with majestic Wolfram Mathematica, so i write this ...
1
vote
1answer
57 views

Entering an differential equation in a Manipulate box

Does anyone have an example of a Manipulate demonstration where the user can type into a box the differential equation, time interval, initial condition, and the result is plotted? This possible in ...
2
votes
0answers
61 views

Differential Geometry on a MeshRegion

For many many years (honestly, since 1987) I've had my own MMa computational geometry code for dealing with 3D meshes. I principally (there's a joke there somewhere) use it to calculate coordinate ...