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

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0answers
13 views

No analogue for Maple's dchange?

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. ...
0
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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 ...
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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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 ...
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0answers
25 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
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
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0answers
105 views

Issue in NDSolve and unknown error

I try to solve a simple BVP: $A {v}''(t)+B v(t)=f(t)$ where $A, B$ — $5\times 5$ matrices, $f(t)$ — 5-dimentional vector-function with the use of NDSolve. Each component of $f(t)$ is a combination ...
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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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
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: ...
2
votes
1answer
104 views

How can I invoke the solution of NDSolve to determine a parameter in my equation just inside NDSlove?

I am trying to solve a differential equation by NDSlove for $h(x,t)$. It reads $$h_t=h_{xx}-V_h-\lambda(t)$$ where $V_h$ is a given function of $h(x,t)$ denoted by ...
0
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0answers
105 views

What is the largest system of PDE you have solved with Mathematica?

I need to solve a system of partial differential equations. In the simplest case it consists of 2000 of PDE equations. In the most complex situation it consists up to 1 million of such equations. ...
0
votes
2answers
77 views

Using parts of piecewise function

I define: f[x_] := Piecewise[{{5, 0 <= x < 10}, {g[x], 10 <= x < 15}, {h[x], x > 15}}] Then I try to solve ODE: ...
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
79 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 ...
0
votes
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 ...
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 ...
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?
2
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5answers
173 views

Simplify an integral involving trigonometric functions

We were doing variation of parameters in differential equations tonight and had to do the following integral, the result given by hand calculations. $$\int \cos t\tan^2 t\,dt=\ln|\sec t+\tan t|-\sin ...
-1
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1answer
72 views

Using InterpolatingFunction in equations

I tried to use InterpolatingFunction in another ODE, but it doesn't work, because it seems for Mathematica that 2 functions are unknown instead of one. ...
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 ...
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
62 views
1
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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 ...
0
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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)}} ...
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: ...
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 ...
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
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 ...
0
votes
1answer
133 views

A good choice to find solutions of ODE

In order to rephrase the question. I would ask you to take a look at the following problem: I have this system of ODE: $$ \begin{cases} \dot{x}(t)= x(t)[r_1(t) -b_1(t)x(t- \tau(t)) - c_1(t)y^m(t)] ...
1
vote
1answer
192 views

Defining a curved region for NDSolve

I have an equation to solve using NDSolve which involves two parameters: $en$ and $k$. The equation produces a set of curves when $en$ is plotted against $k$. In ...
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
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
1answer
721 views

Integro-differential eqn with double integral

I am looking at the following variation of a integro-differential, with y[0]=1. The output is not great, any solutions to this? ...
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: $ ...
9
votes
4answers
387 views

Should DSolve always return solution with constant of integration?

Bug introduced in 10.0.0 and fixed in 10.0.2 Clear[y,x]; DSolve[D[y[x], x] - y[x]^2 + y[x]*Sin[x] - Cos[x] == 0, y[x], x, GeneratedParameters -> C] or ...
1
vote
1answer
76 views

Failed to create a special random-disturbed initial condition for partial differential equation

I try to use BSplineFunction to creat a initial condition for NDSolve which has periodic boundary condition, that is realized by ...
9
votes
1answer
598 views

NDSolve::ndcf: Repeated convergence test failure. How to solve?

I am trying to simulate a system of $n$ pendulums with some friction in Mathematica 9. This is the code I am using: ...
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 ...
7
votes
1answer
206 views

Problem with Neumann condition in quarter disc

Bug persists through version 10.1 So I'm following the available examples in version 10 for FEM, The plane stress operator is shown as this ...
6
votes
1answer
365 views

Poisson PDE over a irregular region with FDM

The problem modeled by the Poisson PDE is related to the torsion of prismatic beams and I use the Finite Differences Method (FDM). I've managed to solve the equation over a rectangle region with ...
0
votes
3answers
118 views

How to define a function

How can I define a function which depends on a function of x? Something like this f[u[x]_,u[x]']= u[x]' + a [x] u[x] +b[x] I think I wasn't enaugh clear. If I ...
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 ...