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

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4
votes
1answer
65 views

How to use DSolve with vectors without decomposing into vector components?

Given a basic, two-dimensional ballistic trajectory problem, I can solve the equations of motion using DSolve (or NDSolve) by ...
2
votes
1answer
137 views

Coupled non-linear differential equations

I have a system of coupled nonlinear differential equations to solve: $$ \frac{\partial m(x,t)}{\partial t}+v(x,t)\frac{\partial m(x,t)}{\partial x}=-\gamma \frac{\partial^2 v(x,t)}{\partial x^2}, \\ ...
0
votes
0answers
80 views

Finding roots by solving its ODEs [duplicate]

Roots of fluctuating function (p,q real) needed to evaluate eigenvalues of $$ y(x) = \dfrac{\sin px }{p} + \dfrac {\sin q x }{q} =0 ...(1*) $$ form a real and complex infinite set. The way to ...
3
votes
2answers
180 views

How to propel the integration of time a little bit further? Numerical solution can not evolve to the max time

I try to solve a nonlinear partial differential equation. I obtain a numerical solution which can not continue to the max time I set, I always receive message NDSolve::ndcf: Repeated convergence ...
1
vote
1answer
37 views

Value of event function not a real number

I am having some problems with handling an event during NDSolve. The event itself is simple, I am looking for when one of my coordinates, defined in ...
1
vote
0answers
76 views

Linear System with Complex Eigenvalues

My students will need to do the following work by hand. \begin{align*} x_1'&=-\frac14x_1+2x_2,\quad x_1(0)=1\\ x_2'&=-8x_1-\frac14x_2,\quad x_2(0)=1 \end{align*} They set it up in matrix ...
1
vote
0answers
58 views
0
votes
0answers
41 views

Two identical expressions for ODE, two distinct result

I have a problem in solving ODEs: two identical expression provides me different answers! I have no idea what's going on, can any one give me some reason why the following two expressions are ...
0
votes
0answers
49 views

Phase Portraits

If possible I want to create several phase portraits like this: ...
7
votes
2answers
305 views

Click in a vector plot to plot several solutions of a system of differential equations

I am aware of the Locator button and I am aware of the Equation Trekker package, but they are not what I want to use. Here is what I specifically want to know how to do, if possible. Consider the ...
7
votes
3answers
284 views

Find the eigenvalues for an ODE

For example, say I have $y'' + \lambda y = 0$ and the endpoint conditions are $y'(0) = 0$ and $y'(\pi) = 0$. How can I find the values for $\lambda$ that for which there is a non-trivial ($y\neq0$) ...
0
votes
1answer
39 views

Simplify huge output or using the output without showing it in full [closed]

I'm trying to solve a system of differential equations. It works fine but Mathematica creates a huge output, which, when shown in full, results in a file size about 100 mb. Using Simplify doesn't work ...
2
votes
0answers
85 views

System of Partial differential equations

I am trying to solve numerically a system of 3 partial differential equations and I am facing a problem. My functions are f[x,t], ...
1
vote
2answers
55 views

Using manipulate with a defined funtion to solve a ODE

As many in this community I'm new in Mathematica and while exploring the numerical solver for differential equations, I tried: ...
6
votes
1answer
709 views

Schroedinger eigenvalue problem in two dimensions (Harmonic Oscillator)

I read here, the discussion about how to solve one dimensional eigenvalue problem. I am wondering, how can one generalize these methods to two dimensions. For example: ...
0
votes
3answers
100 views

Delay difference equation

How can I correctly specify and solve a system of delay difference equations in mathematica similar to NDSolve with regard to delay differential equations? For example if I want to "see" the values ...
2
votes
1answer
263 views

Finding the eigenfunctions of one and two dimensional Harmonic Oscillator

(Edited) For finding the ground state wave function of: $ H\psi(x) = (-1/2)d^2\psi(x)/dx^2 + (1/2)x^2\psi(x) = E \psi(x)$ I have written: ...
23
votes
3answers
601 views

Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?

Given a closed curve $\mathcal C$ in three dimensions, is it possible to use Mathematica's built-in functionality to compute a minimal surface whose boundary is $\mathcal C$? For simplicity, let us ...
3
votes
1answer
137 views

How to solve Laplace equation in 3D?

Basically I want to solve Laplace equation for truncated octahedron in a cube matrix. The boundary condition is Concentration u=200 at surface of truncated octahedron and u=15 at boundary of cube. I ...
0
votes
1answer
102 views

Implicit differentiation and the Folium of Descartes [duplicate]

Given the function (Folium of Descartes) $x^3 + y^3 = 3xy$, how would I find the equations for tangent and normal lines at the point $\left( \frac{3}{2},\frac{3}{2} \right)$? I know that I must use ...
0
votes
1answer
79 views

Phase Portrait Trajectories

How do I make a phase portrait which looks like the ones demonnstrated here? Not the fancy version where I can use the controls to change it, just a screen-shotted version of say a spiral point? Any ...
0
votes
0answers
54 views

Solving a system of differential equations using NDSolve

I am trying to model the descent of a diver jumping from space, and have the following system of equations: ...
0
votes
0answers
32 views

DSolve of the system of two equations with known constants

In my previous post DSolve solution of two unknowns we conclude that Math 10 obtained results fast and that Math 9 did not give the solutions at all after one day. Now I have a problem if there are ...
2
votes
0answers
66 views

DSolve solution of two unknowns

I have one problem with the solution of the system of two differential equations. I waited hours, but Mathematica didn't give me a solution. Is there any way to obtain the results if we suppose that ...
-2
votes
1answer
47 views

Find constants of differential equations [closed]

I have the equation $y'' + 16y' + 64y = 0$ Repeated root of aux eqn $r = -8$ Given the initial conditions, how do I solve for the constants $A$ and $B$? ...
0
votes
1answer
50 views

Solving coupled ODEs with NDSolve

Given the system of differential equations: $i\frac{d}{dt}c_{1}(t)=H_{12} E(t)e^{(iw_{12}t)}c_2(t)+H_{13} E(t)e^{(iw_{13}t)}c_3(t)$, $i\frac{d}{dt}c_{2}(t)=H_{21} E(t)e^{(iw_{21}t)}c_2(t)+H_{13} ...
7
votes
3answers
303 views

Envelope for harmonic oscillator [duplicate]

I am able to take the expression $\cos 11t-\cos 12t$ and use the sum to product identity to write it in the form $$\left(2\sin\frac t2\right)\sin\frac{23}{2}t.$$ I can then plot the function and use ...
1
vote
1answer
126 views

error DSolve::dsfun: cannot be used as a function

I tried to solve system of ODEs, but something was wrong. ...
1
vote
1answer
51 views

WhenEvent error in NDSolve

I’m trying to solve a discontinuous differential equation where there are lost of energy when the trajectory cross the discontinuous manifold. The code I used was ...
0
votes
0answers
32 views

NDSolveValue:dsvar error in a system of non linear differential equations generated using a Table

I have a system of 4 non-linear differential equation, that I generate using Table command. On solving, I keep getting a dsvar error that is not going away. I debugged my code and figured it has to do ...
5
votes
2answers
86 views

Initial time as parameter in ParametricNDSolve

I need a help with the function ParametricNDSolve. My goal is solve the equation \begin{array} &&\dot{x}(t) = y(t) \\ &\dot{y}(t) = x(t)-1-\varepsilon Cos(\omega t) \\ &x(t_0) = x_0\\ ...
4
votes
1answer
384 views

PDE with Stefan Conditions, a.k.a variable boundary

I want to solve the one-dimensional one-phase Stefan problem, but I don't know how to make Mathematica understand the conditions. If you are not familiar with what I'm asking please refer to this ...
7
votes
0answers
2k views

Integro-differential equation

I have to numerically solve a nonlinear partial integro-differential equation using Mathematica. This is my equation, $$\frac{\partial y(x,t)}{\partial t}=\int_{-\infty}^\infty K_0(|x-u|) ...
17
votes
4answers
1k views

How to splice together several instances of InterpolatingFunction?

I have a set of InterpolatingFunction returned by NDSolve which are valid over different (but overall continuous) domains. How ...
0
votes
1answer
95 views

How to solve and plot this 2nd order non linear ODE? [closed]

Is this the correct way to plot the solution of this ODE from $(-8, 8)$? $$y'' - (1 - (y')^2)y' + y = 0$$ ...
0
votes
1answer
47 views

NDSolve emitting error message NDSolve::ndnum [closed]

I am trying to solve this system equn1 = ψ'[x] == - Elec[x] equn2 = Elec'[x] == - ((di/ a)^2)[(Exp[ψ[x]] - (x/(xoi*Sqrt[-ψ[x]])))] For that I am using ...
2
votes
1answer
55 views

How to write ODE to standard form?

Package like odepack needs the ODE written in standard form, which means write the high order ODE to first order ODE equations. The steps of converting ODE to ...
0
votes
0answers
38 views

Graphics Plotfield

A number of older books use the command: <<Graphics`PlotField` But Mathematica 10.0.2 says it cannot find it. Now, I know VectorPlot, but I am wondering if ...
0
votes
1answer
107 views

Generate a small random disturbance on a flat surface for NDSlove

I want to generate a small random perturbation on a flat surface defined on a square domain, e.g. 1 + 0.05 rand(x,y), which can be used as initial condition with periodic boundary conditions in ...
1
vote
2answers
113 views

Linearization of differential equations

I was wondering if one could define an operator such that, when I give a certain number of (differential) equations as an output, and an "equilibrium" value for each of the variables, it returns the ...
0
votes
1answer
102 views

Solving Integro-Differential equations

I need help solving this equation. Is there a built in function that solves this type of equations? DSolve wouldn't work. Updated equation: ...
0
votes
0answers
886 views

PDE problem with initial and boundary conditions

I'm new to mathematica and I don't know what I do wrong, I have written the following PDE problem, with both initial and boundary (four in total) ...
0
votes
1answer
52 views

Unable to break out of two Do loops

I wrote a mathematica program to solve one dimensional schrodinger equation for particle in box model with zero potential. I used two do loops to achieve the task. The inner do loop will solve ...
-1
votes
1answer
76 views

amplitude-phase modulation equations solution

I am trying to solve the following equation ...
0
votes
1answer
79 views

Use ParametricNDSolve with Plotting

I am attempting to solve a differential equation of the form $$ \frac{dx}{dt}=ax+by \\ \frac{dy}{dt}=cx $$ with parameters $0<a<1$ and $a,b,c \in \mathbb{R}$. I am able to use NDParametric ...
2
votes
2answers
135 views

How to change the form $A\cos \omega t + B\sin \omega t$ into the form $\sqrt{A^2+B^2}\cos(\omega t-\phi)$ [duplicate]

I'm preparing notes for teaching next week's class in differential equations. My hand calculation solution of $$y''+192y=0, y(0)=1/6, y'(0)=-1$$ is $$y=\frac16\cos 8\sqrt3 t-\frac{\sqrt3}{24}\sin ...