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

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1
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2answers
18 views

how can I create function which contains a ODE system and its numeric solution

I have create a function like this,which contains a ode system. And I want to know the effect of different parameters ...
1
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1answer
30 views

Plotting 2nd order ODE solution for specific values of constants

Suppose that I have a 2nd order, linear ODE and I want to plot the solution I found using DSolve. How can I plot giving specific values of ...
0
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1answer
55 views

Plot an ODE solution for a list of specific constants [on hold]

Let's say I have a 1st order ODE and want to plot the solution. What I have been doing until now is: ...
6
votes
2answers
143 views

Plotting separatrices for nonlinear system

Consider the system: \begin{align*} x'&=(1-x-y)x\\ y'&=(4-7x-3y)y \end{align*} The system has a saddle point at (1/4,3/4). How can I plot the separatrices on the phase portrait having domain ...
4
votes
2answers
71 views

Kernel quits without error in NDSolveValue

I am using the latest 10.1. The following single line command makes the kernel quit without error message (just a beep): ...
16
votes
1answer
298 views

Analogue for Maple's dchange - change of variables in differential expressions

Maple owns an interesting function called dchange which can change the variables of differential equations, but there seems to be no such function in Mathematica. ...
1
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1answer
51 views

Error with using NDSolve [duplicate]

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

Solving coupled differential equations with an eigenvalue

I have 2 coupled differential equations with an eigenvalue Ei and want to solve them ...
0
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2answers
35 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
104 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
33 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
27 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
votes
1answer
43 views

NDSolveValue with Map

I have: ...
0
votes
1answer
70 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
105 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
votes
0answers
38 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
58 views
0
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2answers
47 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
75 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
83 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
155 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
64 views

DSolve response with DSolve

I'm trying this code ...
1
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1answer
86 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
33 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
72 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
319 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
44 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
141 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
49 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
votes
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
111 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
57 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
votes
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
62 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
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0answers
36 views

Error message for FEMStiffnessElements

I am trying to solve this pde numerically with Mathematica: ...
2
votes
2answers
81 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
77 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
120 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
68 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: ...