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

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1
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1answer
200 views

Solving wave PDE

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

Pade approximants for Taylor series using mathematica [closed]

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
31 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
37 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
78 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
72 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
84 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
190 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 ...
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
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
168 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
70 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 ...
14
votes
2answers
239 views

What can one do with extremely stiff problem in NDSolve?

Consider the following illustrative problem: $$ \frac {\partial f} {\partial t} = \frac {\partial} {\partial x}(x f) + \frac {\partial} {\partial x}(f \frac {\partial f} {\partial x}) $$ This is ...
2
votes
3answers
110 views

Strong glitch with Evaluate in Manipulate

I'm experiencing a strong evaluation problem for a Manipulate box and I can't find the best solution yet. Here's a MWE to show the glitch : ...
0
votes
1answer
57 views

Using Neumann boundary conditions

I had a semi-related physics problem I needed to solve analytically (which I have already done), but I am now curious how I would go about numerically solving the entire system in Mathematica. ...
0
votes
1answer
47 views
0
votes
2answers
277 views

Why the result by hand is different from the built-in DSolve?

Yesterday, I used Mathematica to solve a differential equation using the built-in command DSolve[]: ...
5
votes
0answers
121 views

DSolve breaks when the ordering of independent variables aren't proper?

Bug introduced in 5.2 or earlier and persisting through 10.4.1. I encountered this when trying to solve this problem with DSolve: ...
35
votes
3answers
1k 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
0answers
25 views

How should I solve this system of equasions? [migrated]

I have the system of differential equasions: $$\begin{cases} I_1 \ddot{\varphi_1} + b_1 \dot{\varphi_1} + c(\varphi_1 - \varphi) = M \\ I_2 \ddot{\varphi} + b_2 \dot{\varphi} + c(\varphi - ...
0
votes
0answers
43 views

Problems with numerical solution of differential equation

I'm trying to obtain a numerical solution for my differential equation. But i have the following mistake: Encountered non-numerical value for a derivative at z == 0. Can somebody help with that? ...
5
votes
2answers
249 views

Lagrangian to Hamiltonian

I want to go from Lagrangian description to Hamiltonian one. Using the example given by Mathematica I do something like : ...
3
votes
2answers
67 views

DiscretizeRegion does not include the boundary specified in ImplicitRegion (10.1)

I am trying to do some 3D PDE solving, and I keep running into problems with boundary conditions because my meshed boundaries are not what I expected. For example, the following code ...
0
votes
0answers
44 views

Fitting 6 differential equations to 6 sets of data

I am using the newest Mathematica and I am trying to fit a set of 6 linear differential equations to a set of experimental data for each of the six variables. I am a baby beginner at this and could ...
0
votes
0answers
47 views

NDSolve mixing many scalar and vector equations

I have a system of coupled PDEs, representing the behaviour of 2-dimensional inextensible rods, which I am discretizing using Method of Lines. This gives me a set of ODEs for the inner spatial points, ...
1
vote
1answer
70 views

Discontinious Boundary condition NDsolve

Assume we have any PDE to be solved on the rectangular domain $0<X<4$ and $0<y<2$ How do we tell Mathematica to impose the following boundary conditions? $U[0,y,t]=0, if, 0<y<1, ...
0
votes
0answers
40 views

Impose conditions on differential equations

This is my first post in Mathematica Stack Exchange, so thanks for your help and sorry for any rookie mistakes. I am solving the Einstein equations for two vectorial pertubations h_Alpha and v_Alpha ...
1
vote
1answer
211 views

Using the Levenberg - Marquardt algorithm to minimize a user-defined function

I wrote a function in Matlab that optimizes another user defined function using lsqnonlin with 'levenberg-marquardt' option. Now, I'd like to use the first to ...
2
votes
1answer
44 views

Clearing Problem with DSolve

Consider: This is a classic mistake (using a single equal sign) that has been discussed on Mathematica Stack Exchange before. I know that Clear[Derivative] will cure the problem. However, consider ...
1
vote
1answer
38 views

“MemoryAllocationFailure” in DSolve

Mathematica 10.4, Windows 10, 6 GB RAM, 64 bits When I trying to solve DSolve[{v'[t] == 100 - 0.15 v[t]^2, v[0] == 30}, v[t], t] I get ...
0
votes
1answer
27 views

NDSolve point animation not working [closed]

The below code plots the path of a ball bouncing but loses 90% of its velocity each time it bounces. (adapted from https://reference.wolfram.com/language/ref/WhenEvent.html). ...
0
votes
1answer
91 views

Plotting graphical analysis of chaotic behavior

I am trying to plot some results of chaotic behavior in a system based on a paper for one of my classes. I am a physics undergrad. I found some sample code online springy.nb which I have been trying ...
20
votes
2answers
363 views

Numerical optimal control

I was hoping to tackle optimal control using Mathematica in order to learn how I can use Mathematica's built in numerical integration and optimization functions together in order to solve an optimal ...
3
votes
1answer
63 views

Dsolve svars error: Equations may not give solutions for all “solve” variables

New to Mathematica, trying to solve a set of coupled differential equations related to a geodesics/Calculus of Variations problem. More specifically, I am trying to solve the two Euler-Lagrange ...
0
votes
1answer
57 views

I am having trouble with the DSolve function [closed]

DSolve[{x''[t] + 0.01 x'[t] + x[t] == E^(It), x[0] == 1, x'[0] == 1}, x[t], t] This give the following error :"Equation or list of equations expected instead ...
2
votes
0answers
56 views

How to change the boundary condition near singularity

The following system has a singularity around $x=0.451$. What I want to do is to detect when the solution gets close enough to this singular point (in this example I'm using the threshold of $0.001$), ...
1
vote
0answers
49 views

DSolve does not give an analytic solution for a tutorial input [closed]

I am just starting with Mathematica and I have tried to solve PDE following DSolve, with first three inputs from the Elliptical Partial Differential equations ...
0
votes
0answers
57 views

Nonlinear PDE system in a rectangle

This question is posted by two physics students working together. We are having some trouble while trying to solve Navier-Stokes equations, The main problem is that, while our set of partial ...
0
votes
1answer
91 views

How to omit the corrupt value in a program?

I've such errors: Coordinate .. is not a floating-point number and can't correctly fix it. The problem occures when x==Log[2] The program works correctly ...
0
votes
0answers
63 views

Graphical Representation of Derivatives [migrated]

We know that the derivative function takes as its input a function and gives out another one. The output function is the rate of change of the input function wrt the independent variable which changes ...
0
votes
0answers
53 views

NDSolve for an (slightly) discontinuous Piecewise input

I define a Piecewise discontinuous function V[f[t]], which depends on a function f[t] I want to get numerically using ...
0
votes
1answer
856 views

Solving coupled eigenvalue differential equations [closed]

I am trying to solve an equation of the form as follows $\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\sin^{2}\left(z\right) & z\\ z & ...
2
votes
1answer
114 views

Differential Equation with Numerically Integrated Boundary Conditions

I have a second order differential equation that I'd like to solve numerically, and then integrate its solution twice to get the parametric equations of a curve. The ODE is: $2 ...