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

learn more… | top users | synonyms (3)

0
votes
1answer
10 views
0
votes
0answers
10 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
16 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 ...
9
votes
1answer
103 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
21 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
51 views
0
votes
0answers
32 views

NDSolve won't stop running

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
49 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
57 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 ...
-3
votes
0answers
68 views

Bifurcation diagram for delayed dynamical system

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
0answers
29 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
66 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
63 views
0
votes
2answers
78 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
256 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
39 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 [on hold]

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
185 views

Solving wave PDE

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

Pade approximants for Taylor series using mathematica

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
86 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
27 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
32 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
72 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
31 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} + ...
4
votes
1answer
67 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
34 views

System of partial differential equations using Mathematica [on hold]

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
77 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
177 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 [on hold]

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? [on hold]

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
61 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
225 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
106 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
0answers
44 views

Prey-predator equations [closed]

I'm trying to solve a prey-predator using DSolve for x[t] and y[t]. Here's what I have: ...
0
votes
1answer
53 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. ...
-1
votes
0answers
62 views

Plotting points with Euler's Method [on hold]

I have the solution for this diff. eq. graphed and assigned to a variable, how do I show points on or off the graph? (dy/dx)=(y^2)-(x^2) It's solution is a Bassel Function conglomeration. Now ...
0
votes
1answer
46 views
0
votes
2answers
275 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
120 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: ...
2
votes
1answer
88 views

solving Stokes equations for Force=0 boundary condition

Say you want to solve the movement of a particle in a viscous fluid such that the force on the particle is zero. In general, the solution is trivial since one has no-slip boundary conditions, ie the ...
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
40 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
247 views

Lagrangian to Hamiltonian

I want to go from Lagrangian description to Hamiltonian one. Using the example given by Mathematica I do something like : ...