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

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-1
votes
1answer
385 views

Problem with #1's in DSolve

I've entered the following functions into my notebook, but the solution to them contains #1's that I can't seem to make any sense of. The functions are: ...
0
votes
1answer
43 views
24
votes
1answer
634 views

Calculating a potential function using the finite element method

This is my first attempt to use the Finite Element method available in version 10. There are questions and I am very open to suggestions. My example is flow around a cylinder which is a well known ...
3
votes
1answer
70 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
83 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
41 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: ...
9
votes
2answers
190 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. ...
0
votes
1answer
48 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 ...
-1
votes
1answer
127 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 ...
0
votes
1answer
134 views

Defining a curved region for NDSolve

I have an equation to solve using NDSolve which involves two parameters: $en$ and $k$. The equation produces a set of curves when $en$ is plotted against $k$. In ...
1
vote
1answer
681 views

Integro-differential eqn with double integral

I am looking at the following variation of a integro-differential, with y[0]=1. The output is not great, any solutions to this? ...
1
vote
1answer
99 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
55 views

Third-order ODE with NDSolve

I would like to use NDSolve to draw the integral curve of a third-order ODE ...
1
vote
1answer
59 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: ...
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 ...
1
vote
0answers
71 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
1answer
51 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 ...
4
votes
5answers
240 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: ...
0
votes
3answers
73 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: ...
0
votes
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). ...
4
votes
1answer
240 views

Differentiating ParametricNDSolve solutions

Is there any way to differentiate a solution obtained by ParametricNDSolve? For instance, I have the position $\phi_\gamma(t)$ as a function of time, parametrized ...
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
40 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: } ...
2
votes
2answers
55 views
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
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 ...
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: ...
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: ...
1
vote
1answer
76 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
73 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
72 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
2answers
138 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 ...
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 ...
2
votes
1answer
110 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) ...
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? ...
8
votes
1answer
342 views

Modelling the effect of a structure on a “tsunami” (hyperbolic wave equation)

So, the hyperbolic wave equation can be quite easily solved in Mathematica like this: ...
0
votes
2answers
81 views

NDSolve ensemble of initial points

I want to illustrate how the differential equation depends on the initial conditions. First if all differential equations: ...
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 ...
1
vote
2answers
242 views

Trying to model Heat flow trough different materials with NDsolve

What I'm trying to achieve is model of the heat flow, in this case for the simplest 1D case,its relatively easy to do for the steady state case, but when I try to do it with NDsolve so I get the ...
7
votes
1answer
183 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
2
votes
2answers
397 views

Trying to solve a differential equation with a piecewise initial condition

I am trying to solve $$u_t=\frac{1}{4}u_{xx}$$ $-\infty<x<\infty,\: t>0$ With the initial condition $u(x,0)=\phi(x)$ where $$ \phi(x)= \left\{ \begin{array}{lr} 1 & ...
-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 $s$ ...
0
votes
0answers
59 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) ...
6
votes
2answers
136 views

How to use WhenEvent with a vector ODE in NDSolve

I have an ODE system I'd like to specify as a vector equation in NDSolve. I'm not clear on how to use WhenEvent for a system ...