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

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3
votes
1answer
86 views

NDSolve grid refinement for PDEs

I am experiencing trouble when trying to solve a PDE for various parameter values within mathematica: The PDE in principle can easily be solved numerically, however the stepsize of the spatial ...
1
vote
1answer
94 views

Integral Curve Question using Contour Plot

The ODE $$(xy-2)+(x^2-xy)y'=0$$ is NOT an exact differential equation. However, if I multiply both sides by an integrating factor $\mu=1/x$, the resulting equation ...
1
vote
2answers
43 views

Filling a region defined by a reduce command

I'd like to shade the region defined in the xy-plane produced by this code: ...
1
vote
0answers
104 views

Simulate a polygon bouncing with collision detection inside a circle/polygon

Simulate a polygon bouncing with collision detection inside a circle/polygon. the example can be see in help page by searching WhenEvent; ...
0
votes
1answer
52 views

PDE raises NDSolve::ntdvdae, then kernel quits

In a related question, the SolveDelayed->True option seemed to solve the problem. SolveDelayed is not a valid option in M10 ...
9
votes
2answers
202 views

Solve a PDE over a region defined by a Bezier patch

I am using NDSolve to find the solution to a PDE over an arbitrary domain. The domain is specified by a Bezier patch. ...
-1
votes
1answer
131 views

Small mismatch in theoretical vs MMA solutions of a damped harmonic oscillator differential equation

I solved the differential equation $$ \ddot y + 0.43 \dot y + y =0.1 \cos(2x), \quad y(0)=1,\ \dot y(0)=1 \quad(0) $$ using both the theoretical results from wikipedia and using MMA (I also tested ...
1
vote
1answer
69 views

How can I simplify the result of a differential equation by using my own defined expressions? [duplicate]

I want to solve the following differential equation with mathematica: α β * w''''''[ξ] + ( 1 + α - p ) * w''''[ξ] + p/β * w''[ξ] = 0 The answer seems at ...
1
vote
1answer
118 views

Solving a nasty partial differential equation

I have a differential equation that I would like to solve numerically in the region $z \in [0,L]$ and $t \in [0,t_{max}]$: $$ \partial_t S(z,t) = f(z)S(z,t) + \int_0^L \text{d} z'g(z,z') S(z',t), $$ ...
0
votes
1answer
60 views

Third-order ODE with NDSolve

I would like to use NDSolve to draw the integral curve of a third-order ODE ...
0
votes
1answer
97 views

NDSolve with initial condition: initial conditions did not evaluate to an array of numbers of depth 1(for 1D) or 2 (for 2D) on spatial grid

I have the following naive code to solve a PDE in two spatial dimensions (x,y) with periodic boundary conditions: ...
1
vote
1answer
63 views

DSolve for Second Order Differential

I have an equation y''[t] + w^2*Sin[y[t]] == 0 So I'm using DSolve like this: ...
0
votes
1answer
54 views

Simplifying an answer returned by DSolveValue

Consider the IVP: $$x'=\frac92-\frac{x}{300+2t},\quad x(0)=0$$ Working the solution by hand, the answer is: $$x(t)=450+3t-\frac{4500\sqrt3}{\sqrt{300+2t}}$$ Entering code and then attempting to ...
3
votes
0answers
70 views
4
votes
5answers
244 views

Plot all curves in a table with a single color

I want all of my solutions in a table to be the same color. My attempt: ...
1
vote
0answers
76 views

System of differential equations [closed]

I have to solve the following system of two differential equations with certain parameters inside which I just put them together for simplicity and called them t: ...
0
votes
3answers
77 views

Trouble using Manipulate and NDsolve for coupled ODE's

I'm aware that there are a few threads on the topic of solving coupled ODEs using NSolve and Manipulate. Based on those, I wrote the following code, solving my system of equations: ...
5
votes
2answers
154 views
0
votes
0answers
54 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
55 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
41 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
138 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
40 views
2
votes
2answers
57 views

Strange behavior with Show command

I enter this: ...
1
vote
1answer
81 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
192 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
137 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
44 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: ...
23
votes
3answers
571 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
82 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
95 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
75 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
112 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
154 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
119 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
214 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
86 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
108 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
63 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
202 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
92 views

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

I want to solve this equation, for $r$: ...
0
votes
0answers
67 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
81 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
132 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
86 views

Solving a system of ODEs with DSolve

I am trying to solve a system of ODEs using DSolve ...
0
votes
2answers
54 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
246 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
311 views

How to prevent instability blow up in NDSolve?

I have the following code to solve a PDE: ...
0
votes
0answers
79 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 ...