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

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2
votes
1answer
52 views

Does NDSolve iterate faster in a region where the system being solved is in equilibrium?

I was wondering how exactly the time it takes for NDSolve to iterate through a certain region of the domain depends on the local behaviour of the given system being solved. My guess would be the ...
0
votes
0answers
32 views

How to speed up NDSolve?

I have a program where I need to iterate NDSolve thousands of times for different configurations of a diffusion problem. The thing is, I only need about 3 digits of accuracy. I looked thru previous ...
0
votes
0answers
39 views

Lyapunov exponent of non-autonomous differential equation

I am trying to calculate the Lyapunov exponent for a non-autonomous system using M Sandri code, but it always shows me error "infinite expression 1/0 encountered". Does anyone know about this? Mr. ...
3
votes
1answer
185 views

Solve a nonlinear PDE equation with a Neumann boundary condition

I am trying to use Mathematica 10 to solve a PDE $$u_t=u_{xx}+u_{yy}+u(1-u),$$ in the unit disk $(x,y) \in D=\{(x,y):x^2+y^2<1\}$, with the Neumann boundary condtion $$\frac{\partial u}{\partial ...
6
votes
1answer
105 views

Constrain Locator to specified region

How can I constrain the locator to stay within the region defined by RegionPlot? When the Locator remains within the region, ...
13
votes
3answers
469 views

Particles bouncing in a 3D box

I made this Manipulate code which shows a pack of particles randomly moving inside a box. It has a huge performance issue. What should be the best way in doing ...
0
votes
1answer
111 views

Trouble solving a system of 2 ODE's with NDSolve

I'm trying to solve a system of two coupled second-order ordinary differential equations using Mathematica's NDSolve. The functions of r that appear in the equations are ...
10
votes
2answers
2k views

Error entering equation in DSolve

I entered a command incorrectly as follows: DSolve[{y'[x]=y[x]},y[x],x] I am now experiencing: ...
0
votes
1answer
33 views

Trying to solve ODE. Need help with error messages [on hold]

With this code I get an error-message: Equation or list of equations expected instead of True in the first argument. Apparently y'[0] == v0 gives ...
-1
votes
0answers
57 views

Force NDSolve to use finite difference

How to force NDSolve to use finite difference instead of FEM. I have the following code: ...
0
votes
1answer
66 views

Boundary conditions for NDSolve

I get the following message: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >> from ...
0
votes
0answers
42 views

Eigenelements of conductivity equation

I am trying to calculate the eigenvalues and eigenfunctions of the conductivity equation in an annulus. In particular I am looking for $(\lambda, u)$ s.t. $$ \begin{cases} \Delta u = \lambda u & ...
0
votes
0answers
39 views

Getting DSolve to return different solutions [on hold]

I am Using 10.0 I am trying to solve the following ODE: $$ \frac{d^2 \psi}{d\theta^2}+ \nu \psi =0$$ , $$\psi(0)=0$$,$$\psi(3\pi/4)=0$$ and Mathematica only sppits out the trivial solution PS: I am ...
10
votes
1answer
167 views

NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity

I posted a similar question a short time ago regarding the 3D Coulomb problem. Jens' excellent answer to this thread allowed me to obtain the correct eigenvalues and eigenenergies for that system. I ...
-4
votes
0answers
78 views

Bifurcation diagram for delayed dynamical system [on hold]

The delayed dynamical system describe as $\dot{x}(t)=y(t)-ax^3(t)+bx^2(t)-z(t-\tau)+I \\ \dot{y}(t)=c-dx^2(t)-y(t)\\ \dot{z}(t)=r[s(x(t)-e)-z(t)]$ where $a=1.0; b=3.0; c=1.0; d=5.0; r=0.006; s=4.0; ...
0
votes
1answer
33 views
0
votes
0answers
28 views

Setting Initial Conditions in a System of Differential Equations that don't start at t=0

I have a system of six differential equations (linear for the sake of the discussion). I want to set the initial condition to start at time t=18 and not time t=0. I know the values of the dependent ...
0
votes
0answers
28 views

Solving Time-Dependent PDE's Analytically with no non-trivial Boundary Conditions

I'm having some trouble solving a partial differential equation that is supposed to model the propagation of a scalar field in Schwarzschild spacetime using spherical coordinates. I'm using the DSolve ...
5
votes
0answers
42 views

EventLocator in NDSolve seemingly hogs memory in Windows, but not Mac

I have written a function (ftest in my code) which does the following: Takes a vector {x,vx,vy} as input Numerically solves (with high precision) a specific ...
0
votes
0answers
56 views
0
votes
0answers
42 views

NDSolve won't stop running [on hold]

I'm trying to solve the wave equation with NDSolve, but everytime I hit evaluate notebook it won't stop running. Any insights? ...
4
votes
1answer
60 views

Issues with modeling pulses in a very simple system of DAEs

Some time ago I had asked this question about evaluation difficulties using Euler Integration to solve a system of ODE where discrete pulses occur. While I have now abandoned Euler integration and ...
0
votes
1answer
61 views

How to perform this nth derivative operation in MMA?

I have to solve this following equation where I need to differentiate a function $n$ times. $$A=\sum_{n=0}^{m-1}\frac{s^n}{n!}(-1)^n\frac{d^nf(s)}{ds^n}$$ How to express the above equation in ...
0
votes
0answers
33 views

Recycle boundary condition

I'm having the following issue that can not find a solution , by using this boundary condition u[0, t] == 2 u[1, t] that Mathematica does not understand, someone ...
1
vote
0answers
73 views

How to “INJECT” with holding Evaluation, specifically into a WhenEvent

I am importing a set of differential and stochastic equations from an external package, and want to use Mathematica to analyse this. I am struggling building the set of equations that I can use with ...
8
votes
1answer
71 views
0
votes
2answers
82 views

Jump boundary conditions

I'm having the following issue that can not find a solution , by using this boundary condition ...
-1
votes
0answers
21 views

How does d/dx (ln(1/x) + c) = d/dx (c - ln(x))? [migrated]

I have to find the derivative of the following expression ln(1/x) + c it appears the answer is -1/x however i am told it can ...
2
votes
1answer
262 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: ...
1
vote
0answers
42 views

Solving ode which solution oscillate violently

This is a ordinary differential equation: y[x]/(-1 + x^4)^2 - ((1 + 2 x^2 + 3 x^4 - 2 x^6) Derivative[1][y][x])/(x - x^5) + Derivative[2][y][x] == 0 I want to ...
0
votes
0answers
27 views

Solving equations but cannot define argument [closed]

Hi everyone I am new to mathematica and I really need help now. The question is like this: I defined a function H(e1,e2) and I want to solve PDEs like ...
1
vote
1answer
194 views

Solving wave PDE

I am trying to solve the wave PDE with NDSolve. Below is the equation: ...
0
votes
0answers
31 views

Pade approximants for Taylor series using mathematica [on hold]

fluid-dynamics In running Pade Approximants for taylor series to rationalize using Mathematica for higher degrees, the program gets hanged. What can be the reason ?
3
votes
2answers
89 views

Switching Differential Equation in NDSolve

I am trying to solve the following system of differential equations using NDSolve: $\dot{z}_t=.5(1-z_t)$ $\dot{y}_t=.05y_t+z_t-x_t$ subject to the following constraint: $-y_t-z_t\le0$ where $z_t$ ...
0
votes
0answers
29 views

Pass List / Vector argument through NDSolve to a function

I am trying to pass vector or list as argument to the function from NDsolve.And I am getting these error. Also I am pretty new to stack overflow. Apology if this a possible duplicate. Here is my code. ...
1
vote
1answer
34 views

portions of plot missing for a relatively simple function

I am trying to produce a graph of the linear dynamic system response to a step input. The code is as follows: ...
0
votes
2answers
77 views

Free-fall air resistance problem

I´m working on a free fall problem and I got an equation with variable $k$ when the situation has air resistance. Then I compared with no air resistance equation ($-4.9$, considering t variable). So, ...
3
votes
0answers
74 views

Kernel crashes when computing finite difference mixed derivative with respect to y & z but works fine when computing with respect to x & y or x & z?

I am using Mathematica 10.4.0 on Ubuntu 16.04. I am trying to solve a set of differential equations using finite difference method on an NxNxN cubic grid (x, y, z directions). I am getting a weird ...
3
votes
0answers
35 views

Constraining Function to be positive with NDSolve, Allee effect

I am trying to numerically solve the steady-state behaviour of the Allee effect (with one spatial dimension, diffusion): $\frac{\partial n}{\partial t} = D \frac{\partial^2 n }{\partial x^2} + ...
5
votes
1answer
71 views

Finding the correct boundary conditions to a specific problem

I want to reproduce the following problem in the figure: $$\phi''+c\phi'\sqrt{m^2\phi^2+\phi'^2}+m^2\phi=0$$ where $\phi=\phi(x)$ with $x \in (-\infty,\infty)$, $c=\sqrt{3/2} \ $ and $m=0.2$. ...
-5
votes
0answers
36 views

System of partial differential equations using Mathematica [closed]

As you can I am trying to solve a system of partial differential equation using MATHEMATICA. However, I could not. Can anyone provide me with a code which is able to solve such equations in ...
3
votes
2answers
80 views

Assigning Element Markers to 3D FEM Mesh

I have created a 3D graphic using GraphicsComplex and then use ToElementMesh to generate a 3D Mesh that I want to solve a PDE on, but I cannot figure out how to apply ElementMarkers to the Boundaries. ...
10
votes
1answer
186 views

NDEigensystem cannot solve numerically the 3D Coulomb problem, while DSolve returns the right answer

After having derived by hand the eigenvalues and eigenfunctions for the 3D and 2D hydrogen atom, I want to solve the systems numerically using Mathematica. I need to do this because my next step is to ...
-2
votes
0answers
39 views

Finding Laplace Transform [closed]

With the following DE y"(t)+5 y'(t) +6y(t)= t 0 How do I find the Laplace Transform to find the IVP??? I've tried everything and I can't figure it out.
17
votes
4answers
2k views

How do I solve a PDE with a strange boundary condition?

How do I solve the PDE with boundary value like this $$u(t,x,y)=0, \textrm{when } F(x,y)=0$$ using DSolve? As a specific example, I want to solve heat equation $$\frac{\partial u}{\partial ...
0
votes
0answers
247 views

How to solve system of non linear Differential Equations with 1 independent variable and 3 dependent variables? [closed]

I have been trying to solve this system of differential equations using mathematica. $$F(t) B''(t)+B'(t) F'(t)+B(t) F''(t)=0,\\ F(t) A''(t)+A'(t) F'(t)+A(t) F''(t)=0, \\ B(t) A'(t)+A(t) B'(t)=0$$ Here ...
0
votes
1answer
1k views

how to solve second order nonlinear coupled differential equations using NDSolve with hyperbolic function

i have to solve some solitons scattering through this coupled equations. i need to get two different graph, but still the graph did not come out. and also the equations quite complicated containing ...
3
votes
2answers
166 views

Solving coupled differential equations with unknown constants

Is it possible to obtain exact solutions of these types of coupled differential equations directly in Mathematica ...
2
votes
0answers
68 views

NDSolve for unsteady Taylor-Goldstein equation, can't use MethodOfLines

I am trying to solve a relatively simple system of linear PDE in two variables (z,t). The equations are basically the Navier-stokes equations linearized around a constant background velocity profile ...