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

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2
votes
2answers
62 views

Strange behavior with Show command

I enter this: ...
1
vote
1answer
84 views

Preventing complex term in a differential equation solution

I am solving the initial value problem: $$y'=\frac{t+1}{t(t+4)},\quad y(-1)=0$$ I believe the correct answer is $$y=\frac14\left[\ln(-t)+3\ln(4+t)-3\ln 3\right]$$ with an interval of existence ...
3
votes
1answer
230 views

Boundary sphere partial differential equation

I am trying to solve partial differential equation in spherical coordinates $(\theta,\phi)$,but I don't know how to properly include boundary conditions of $\theta$. For $\phi$ it is periodic, but ...
3
votes
1answer
167 views

Fick's Law over Implicit Regions

I'm trying to solve 2D Fick's law of diffusion from the boundaries of a triangle (future shapes will include more complex implicit regions). I'm able to model diffusion without time in complex ...
6
votes
1answer
133 views

Long running ToElementMesh with very “large” domains

I'm trying to solve a system of PDE over a large domain. This doesn't means I need to have a huge amount of mesh points and mesh elements to discretize the domain. Just that the domains has a big ...
4
votes
0answers
54 views

Extraneous reaped data with NDSolve and WhenEvent

In exploring What is the range of values $x$ for which $f(x)$ is higher than $k$ over a given domain?, I came across the following strange behavior: ...
26
votes
3answers
652 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 ...
1
vote
1answer
101 views

Initial Value Problem with initial conditions as closed region

Does Mathematica have functionality to solve an Initial Value Problem when the initial conditions consist of a closed region (rectangle) instead of a point? That is, instead of initial conditions as ...
1
vote
2answers
99 views

Plotting solutions to ODE for continuously varying parameters

I am trying to plot the solution of an ODE with continuously varying one of its three parameters. (I just fixed two of them for simplicity.) Any suggestions? ...
0
votes
1answer
50 views

EllipticF reduction

Is it possible to reduce the following Z to Legendre form Elliptic integral of the First kind? $$ \int \dfrac {\sec u\; du } {\sqrt{ (1- {(\nu \tan u)}^2 }} ..(1*)$$ With ...
0
votes
0answers
28 views

What means the definition F[t_?NumericQ] :=…? [duplicate]

I've come along a function defined in this way: F[t_?NumericQ] := NDSolve[{-u''[x] - u[x]/x == -t^2 u[x], u[x0] == x0, u'[x0] == 1}, u, {x, x0, x1}] What does ...
3
votes
2answers
84 views

Saving a plot as a pdf to use in Latex

I use the following code: sol = DSolveValue[{y'[t] == 1/(2 y[t] + 3), y[0] == 1}, y, t]; Plot[sol[t], {t, -10, 10}, ImageSize -> Small] Then I Ctrl+click the ...
1
vote
1answer
167 views

Runge-Kutta Butcher tables

I like to have the Butcher's table for Explicit (or implicit as well) Runge-Kutta method of a fixed order. I do not understand reading ...
3
votes
3answers
118 views

Differential equation with a Heavisidetheta function running for ever

So I'm trying to get the solution of the following differential equation: ...
1
vote
2answers
202 views

Solving a second order non-linear differential equation

I am trying to solve the following equation DSolve[{u''[t] + 4 u[t] + 0.1 u[t]^3 u'[t] ^2 == 0, u[0] == 1, u'[0] == 1}, u, t] Unfortunately Mathematica is ...
2
votes
1answer
165 views

PDE: Solving Burgers' equation with initial value given by a self consistency equation

I would like to solve in Mathematica the well known inviscid Burgers' equation \begin{align} \begin{cases} u_t(x,t) + u(x,t)u_x(x,t)= 0 \\ u(x,0) = m(x) \end{cases} \end{align} where $$m(x) ...
16
votes
2answers
256 views

Least effort to handle a point source inside the domain of PDE(s)

By point source I mean a constrained condition at one point inside the domain of PDE(s). For example: $$\frac{\partial ^2u(t,x,y)}{\partial t^2}=\frac{\partial ^2u(t,x,y)}{\partial ...
0
votes
2answers
89 views

NDSolve ensemble of initial points

I want to illustrate how the differential equation depends on the initial conditions. First if all differential equations: ...
3
votes
1answer
113 views

DSolve not returning a rule

I am trying to solve a PDE, but the DSolve is not returning a rule. How exactly can I get Mathematica to yield a solution? ...
0
votes
0answers
69 views

Flux continuity with NDSolve

When NDSolve is applied to model mass diffusion (or heat flow) through different materials, is the continuity of flux condition automatically satisfied at the ...
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. ...
7
votes
1answer
215 views

mathematica 10 not showing numerical solution of differential equations?

I just got the new mathematica version 10 and tried to solve the following system of differential equation. $$r^2\frac{d^2f}{dr^2} = 2f(1-f)(1-2f)+\frac{r^2}{4}h^2(f-1)$$ ...
-1
votes
1answer
96 views

Find $r$,in terms of variables $U$ and $V$

I want to solve this equation, for $r$: ...
0
votes
0answers
87 views

Solving for a coordinate transformation for a rank 2 tensor

I am working on a project in general relativity, and I have a metric or rank 2 tensor $g_{ab}$ of the form, $$g =\left( \begin{array}{ccccc} f(x^a) & 0 & 0 & 0 & 0\\ 0 & -f(x^a) ...
-2
votes
1answer
84 views

Ordinary Differential Equation Question [closed]

I was wondering whether someone might be able to point me in the right direction for this ODE that I am trying to solve? It is: $$\frac{du}{dx} = \frac{x}{s}-\frac{1}{2}-\frac{u}{x}$$ with $s$ ...
1
vote
1answer
186 views

Locating Periodic Orbits

Here is the code for the numerical integration of an orbit. First the module for the definition of the equations of motion. ...
2
votes
0answers
133 views

How to control pedestrians to enter the simulation region with random functions?

I am working on simulating crowds of a cross-typed region, given that pedestrians entering from 4 gates of north, east, west and south, ...
0
votes
0answers
88 views

Solving a system of ODEs with DSolve

I am trying to solve a system of ODEs using DSolve ...
1
vote
0answers
95 views
1
vote
1answer
78 views
0
votes
2answers
56 views

trouble with adding a legend to a plot

I am having trouble with adding a legend to a plot. this is my code,I tryed to use serval things,like ...
1
vote
2answers
321 views

NDSolve with Explicit, Implicit Euler and Trapezoidal method

I am using Mathematica 9.0 both on Linux and Windows and I would like to integrate the Van der Pol equation numerically using various techniques such as Explicit and Implicit Euler and Trapezoidal ...
7
votes
3answers
338 views

How to prevent instability blow up in NDSolve?

I have the following code to solve a PDE: ...
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 ...
2
votes
0answers
114 views

DSolve versus DSolveValue [closed]

I've just discovered the new command DSolveValue in Mathematica 10. Is this new command now the preferred instead of DSolve? Is it the better command to teach to students? Same question for ...
4
votes
2answers
153 views

Implement functions that depend on previous value in NDSolve

I want to numerically solve a system of differential equations in Mathematica, say for example $\frac{dx}{dt} = f(x,y,t) \\ \frac{dy}{dt} = g(x,y,t)$ for $x(t), y(t)$. However, the functions depend ...
2
votes
1answer
216 views

NDSolve and maximum number of steps reached

I am newbie at Mathematica but I need to solve differential equation so I took my chances and tried to use this powerful tool to solve this equation: $$\frac{d}{dx}\left([\cos(2\pi ...
1
vote
1answer
183 views

Plot multiple solutions of a system of differential equations with different values of constant c by using NDsolve

I am traying to solve system of differential equations with different values of constant c then plot the solution with different values of the constant c. where c= 2.2758, 2.04822, 1.82064, 1.59306, ...
0
votes
1answer
82 views

To get a certain value of NDsolve of the solution [closed]

I need to solve the differential equations for different values. Once it is solved I want to take, for example, x[29] for each initial condition and plot it as a function of this initial conditions. I ...
5
votes
0answers
139 views

Alternatives to FiniteElement as Spatial Discretization Method for NDSolve

Finite Element Programming: [...] It is possible to skip this section and continue with the discretization stage and make use of the initialized data structures ...
6
votes
2answers
194 views

RegionPlot from NDSolve

I am having quite a headache using RegionPlot to see the region of acceptance of certain coupled differential equation. I shall elaborate and try to be as ...
4
votes
2answers
240 views

Solving a discontinuous differential-algebraic equation system for plasticity behaviour

I need to solve a discontinuous equation which is typical in theory of plasticity. For a simple case I get the following equation system (reformulated for numerical implementation): $s(t) = ...
3
votes
1answer
202 views

Trouble understanding NeumannValue and Inactive/Formal PDEs

I read all documentation about the Finite Element Method in Mathematica 10, and I read some questions here, but I'm still unable to properly understand how to use the ...
1
vote
2answers
165 views

Help to numerically solve ODE

http://math.stackexchange.com/questions/912076/time-period-of-ode Trying to numerically compute and compare the time period of an oscillation with the analytical solution suggested by Robert Israel. ...
5
votes
3answers
138 views

Trouble Discretizing a ParametricRegion; Joukowsky Map and Wing Profiles

I'm trying to compue a mesh of full 2D region delimited by the a circle transformed with a Complex map. ...
1
vote
1answer
75 views

Strange constants in a PDE solution by DSolve

I'm solving the following PDE: DSolve[F''[ξ] + (Ω^2 - M^2 Exp[2 α ξ]) F[ξ] == 0, F[ξ], ξ] And Mathematica gives a general solution in terms of modified Bessel ...
10
votes
1answer
341 views

representation of custom deformation on a meshgrid

I am trying to represent 2D deformations on a rectangular grid. In Mathematica 10, there is a method to solve the elastic differential equations and then represent the deformation as presented here: ...
0
votes
0answers
70 views

EquationTrekker PropertyValue errors

In Mathematica 10.0.2, the basic example for EquationTrekker in the documentation is: ...
1
vote
0answers
228 views

NDSolve: Equation with interpolating function [closed]

I have a question regarding DSolve and NDSolve functions in Mathematica 10. For instance, I'd like to solve an ODE: ...
5
votes
1answer
119 views

Solve a differential equation with an integral inside?

I am trying to solve this differential equation in Mathematica: y'[t]+integral from 0 to t of y[x]dx =e^(-t) where y[0]=0. Is this possible?