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

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5
votes
2answers
148 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): ...
3
votes
2answers
458 views

BC for transport equation using NDSolve

First I can solve a transport equation with a source (Is it still called transport equation?) using DSolve. The form of the source serves only as an example. It can ...
9
votes
1answer
300 views

solve ODE with divergencies

The solutions of the second order differential equation $$\frac{1}{\eta}\frac{d}{d\eta}\left(\eta \frac{df}{d\eta}\right)+\left(1-\frac{s^2}{\eta^2}\right)f-f^3=0$$ is shown in Fig. 5.2 below, for ...
6
votes
2answers
182 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 ...
1
vote
1answer
42 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
votes
1answer
38 views

Problems with DSolve [closed]

I'm trying to solve and plot a second order ODE. Here is my code: DSolve[y''[x] + 4 y'[x] + 12 y[x] == 80 Sin[2 x], y[x], x] Problem 1... it sticks me with a ...
0
votes
1answer
59 views

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

Let's say I have a 1st order ODE and want to plot the solution. What I have been doing until now is: ...
1
vote
1answer
70 views

Error with using NDSolve [duplicate]

I am currently trying to numerically solve a system of differential equations. Here is my code: ...
0
votes
1answer
121 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
votes
1answer
34 views
1
vote
0answers
62 views

Failing to solve a simple PDE with NDSolve

I'm trying to solve the following PDE. Actually this is a major simplification of the original with all x,z dependent coefficients being fixed. For some reason Mathematica (10.0) cannot solve even ...
0
votes
1answer
77 views

Eigen energies of 2D time independent Schrödinger equation

Firstly, I am aware that a similar question of this type was asked, but it was not helpful as it was only one dimensional (so please don't mark my question as a duplicate) The trouble I am having is ...
0
votes
2answers
45 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
0answers
122 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
127 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
1answer
51 views
0
votes
0answers
41 views

Integro differential eq boundary difficulties

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

Why NDSolve cannot solve such a simple set of differential equations? [closed]

I want to solve a set of ODE like below, but Mathematica outputs nothing for this which greatly confused me. WHY? ...
0
votes
0answers
110 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. ...
-3
votes
1answer
67 views
0
votes
1answer
99 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
53 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
128 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
43 views
2
votes
5answers
189 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 ...
0
votes
1answer
96 views
-1
votes
1answer
77 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
77 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
99 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
votes
0answers
69 views
1
vote
1answer
113 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
votes
1answer
67 views

Using WhenEvent

I want to solve this simple equation with a event: ...
0
votes
1answer
83 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
votes
0answers
35 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
votes
0answers
51 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
182 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
159 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
119 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 ...
5
votes
1answer
112 views

NDSolve and FEM support for non conformal meshes of a disk [with Kernel crash]

I want to create an ElementMesh for a disk. For my specific scenario, some author advise to use a regular mesh, where the radial and tangential directions are ...
1
vote
1answer
198 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 ...
0
votes
1answer
129 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 ...
0
votes
0answers
46 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
417 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
4answers
169 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
224 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
385 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
122 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
56 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 ...