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

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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: ...
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: ...
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 ...
1
vote
2answers
156 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
215 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
121 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
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? ...
8
votes
1answer
351 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
87 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
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 ...
1
vote
2answers
271 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
203 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
2
votes
2answers
427 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
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 $s$ ...
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) ...
6
votes
2answers
141 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 ...
3
votes
1answer
200 views

Using WhenEvent for derivative of discontinuous function

I have a discontinuous function ($u(t)$, a square wave) and I would like WhenEvent to trigger when the signal goes high/low, i.e. when the value of $u(t)$ changes. ...
4
votes
2answers
3k views

How can I solve this PDE with initial conditions?

I wish to solve the following second order partial differential equation $$u_{tt}=c^2 u_{xx}$$ with the initial conditions $$u(x,0)=e^x,\quad u_t(x,0)=\sin x$$ In Mathematica, I evaluated the ...
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
87 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
248 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
312 views
1
vote
1answer
157 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
0answers
80 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
104 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
130 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
144 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
2answers
157 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. ...
0
votes
1answer
57 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 ...
0
votes
1answer
173 views

Cannot get specific value from NDSolve (multiple functions)

I am trying to solve six connected differential equations. This is my code: ...
5
votes
2answers
184 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
205 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) = ...
10
votes
1answer
299 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: ...
11
votes
3answers
4k views

Solving a time-dependent Schroedinger equation

I want to solve the time-dependent Schroedinger equation: $$ i\partial_t \psi(t) = H(t)\psi(t) $$ for matrix, time-dependent $H(t)$ and vector $\psi$. What is an efficient way of doing this so ...
13
votes
2answers
977 views

Neumann boundary conditions in NDSolve over nontrivial region

The problem I would like to solve involves diffusion in the following region ...
7
votes
1answer
188 views

Problem with Neumann condition in quarter disc

So I'm following the available examples in version 10 for FEM, The plane stress operator is shown as this ...
0
votes
0answers
52 views

EquationTrekker PropertyValue errors

In Mathematica 10.0.2, the basic example for EquationTrekker in the documentation is: ...
4
votes
1answer
260 views

Understanding of method for NDSolve

I used automatic method for NDSolve. Then I asked myself - which method Mathemathica prefered? I got an answer for this question on this forum, that I need to use: ...
1
vote
0answers
123 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
104 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?
10
votes
2answers
443 views

Water Hammer - Numerically solving system of PDEs

I'm trying to use Mathematica to solve the water hammer effect. ...
9
votes
4answers
351 views

Should DSolve always return solution with constant of integration?

introduced in Version 10.0, fixed in 10.0.2 Clear[y,x]; DSolve[D[y[x], x] - y[x]^2 + y[x]*Sin[x] - Cos[x] == 0, y[x], x, GeneratedParameters -> C] or ...
0
votes
1answer
86 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
1answer
60 views

How can I assign a vector unknown function to solve the ODE system?

I noted that using non-scalar variables is convenient when a system of differential equations is governed by a process that may be difficult to express symbolically. Taking a example from the tutorial ...
0
votes
0answers
150 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 ...