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

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0
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0answers
47 views

Selecting values over lists for discrete inputs in NDSolve

I'm currently trying to simulate a step response in a simple tank system with NDSolve. I would like it to start at say time 2 (the precise time is not important). ...
2
votes
0answers
53 views

NDSolve is running an extremely long time: how can I save the existing data?

I am trying to solve a PDE by the following code. It takes 1 hour or so to reach t=25.72 but about 20 hours to reach t=25.72404031638060174049337306126853310997. Actually, the time step is extremely ...
1
vote
1answer
38 views

Variables within functions within DSolve

Hi I am just beginning to learn Mathematica and this is my first time I have been exposed to any type of coding. I am encountering a problem in a basic physics problem. For example we are always ...
2
votes
2answers
134 views

Too high differential order in boundary conditions?

The following boundary value problem has a unique solution: $$ \begin{cases} x''-x=0\\ x''(0)=0\\ x(1)=1 \end{cases}\\ \text{General solution: } x=c_1 \sinh{t}+c_2\cosh{t}\\ \text{Solution for BVP: } ...
0
votes
0answers
37 views
2
votes
2answers
55 views

Strange behavior with Show command

I enter this: ...
1
vote
1answer
77 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
182 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
128 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 ...
4
votes
0answers
42 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: ...
21
votes
3answers
476 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
75 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
72 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
0answers
27 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
70 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 ...
3
votes
3answers
111 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
130 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
109 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) ...
15
votes
2answers
199 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
79 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
105 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
62 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 ...
7
votes
1answer
179 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
91 views

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

I want to solve this equation, for $r$: ...
0
votes
0answers
58 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
77 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 $s$ ...
2
votes
0answers
131 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
83 views

Solving a system of ODEs with DSolve

I am trying to solve a system of ODEs using DSolve ...
0
votes
2answers
51 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
211 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
283 views

How to prevent instability blow up in NDSolve?

I have the following code to solve a PDE: ...
0
votes
0answers
72 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
86 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 ...
3
votes
2answers
114 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
118 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
140 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
45 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
2answers
178 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
188 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) = ...
1
vote
2answers
154 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. ...
10
votes
1answer
282 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
47 views

EquationTrekker PropertyValue errors

In Mathematica 10.0.2, the basic example for EquationTrekker in the documentation is: ...
1
vote
0answers
80 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
99 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?
9
votes
2answers
367 views

Water Hammer - Numerically solving system of PDEs

I'm trying to use Mathematica to solve the water hammer effect. ...
0
votes
1answer
82 views

Parametric Plotting

I am trying to make a parametric plot of the x and y displacements of a vibration problem. When trying to plot the parametric curve won't show up.
0
votes
0answers
147 views

Time-dependent mesh deformation

I want to display the result of a deformation with a mesh, but I solved the deformation with a time dependency. So I have two functions: uxsol[t,x,y] and ...
3
votes
1answer
139 views

Introduction to Vectors and NDSolve

I want to use NDSolve for a complicated equation that contains vectors. I am still new to Mathematica, and have really enjoyed what I have learned thus far. Concerning this question, I have already ...
2
votes
2answers
75 views

How to generate pure function solution using NDSolve

Suppose i have an equation NDSolve[{ca'[t]== -0.1*ca[t]*cb[t], cb'[t]== -0.1*2*ca[t]*cb[t], ca[0]== 10, cb[0]== 12},{ca,cb},{t,0,5}] how can i get the ...
2
votes
1answer
144 views

Problem solving a nonlinear differential equation with specific boundary conditions

I am trying to solve the following differential equation: DSolve[{y''[x] == A*B (y[x])^2, y'[0] == -B*C, y'[-D] == 0}, y[x], x] For my system, this ...