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

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0
votes
1answer
244 views

DAE - varying initial conditions

I want to solve a DAE-system and I want to vary more than one initial conditions and to manipulate them. I looked here: Putting NDSolve into ParametricPlot But it does not work: ...
19
votes
2answers
964 views

3D orbits and inaccuracy over time

I wrote a little program to use Newton's Law of Universal Gravitation to animate 3 planets orbiting a central star, but I have run into a problem. Here is the code that I used to create the program (I ...
2
votes
2answers
409 views

Mass Symbolic Manipulation with Subscripts? (from plaintext Input)

The simplest example of the change being sought is a greek letter, typed in as plaintext nu, and its may be replaced by the symbol, ν: expr = 3nu*kx*ky+ ...
2
votes
1answer
459 views

How to adjust parameters to experimental data on a NDSolve problem

I have 2 differential equations with 2 variables, x and y,which are a function of t and I have the parameters k1, k2 y k3. ...
8
votes
0answers
491 views

Numerically solve 2nd order differential equation with singularity

Consider a second order differential equation with a potential that diverges at some generic value in the variable. For example: $$-y^{\prime\prime}(s)+\frac1{\mathrm{cn}{(s\mid k^2)}}y(s)=0$$ where ...
5
votes
1answer
136 views
3
votes
2answers
1k views

ODE and BVP: NDSolve errors

The mathematical problem is shown here. I tried to solve writing the ...
3
votes
1answer
989 views

How to plot and solve the numerical solution of a integro-differential equation

I have a integro-differential equation of the form $y'(t) = - \int_0^t {y(t_1 )} e^{t_1 - t} dt_1, {\rm{ t}} \in {\rm{[0,10], y(0) = 1}}$ My code is: ...
1
vote
1answer
483 views

What does the Error Message in DSolve really mean?

Having this ordinary non linear differential equation $$y'-x^2 (y+1)\cdot (y+2)^2= 0$$ with the boundary condition $y(4)=2$. When trying to solve this one with Mathematica by using ...
3
votes
3answers
750 views

Plotting heat equation in a Manipulate expression

I have a 2D heat equation $u_t = \alpha (u_{xx} + u_{yy})$ with conditions: $u(x, y, 0) = 300$, $u_y(x, 0, t) = \mu_1(x)$, $u_y(x, 1, t) = \mu_2(x)$, $u(0, y, t) = \mu_3(y)$, $u(1, y, t) = ...
0
votes
1answer
144 views

Notation for numerical solutions to differential equations

Can somebody explain this notation to me? Using Mathematica's first example in the NDSolve documentation: ...
0
votes
2answers
558 views
1
vote
0answers
286 views

Adapting NDSolve to circumvent NDSolve::bdord: error for 1-D Euler Equations

I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a ...
2
votes
1answer
477 views

Infinite Expression Error from NDSolve

I am trying to solve a differential equation numerically. So I have ...
3
votes
3answers
293 views

Mathematica not able to confirm its own solution to differential equation

I type the following into Mathematica: DSolve[q''[x] + 2 x/(x^2 - 1) q'[x] - 4*q[x]/(x^2 - 1) == 0, q[x], x] It gives me the result ...
2
votes
1answer
272 views

How to integrate ParametricNDSolve solution with respect to a parameter?

I have just upgraded to the new version of Mathematica because of its new built-in ParametricNDSolve function. I need to solve a first-order non-linear ordinary ...
3
votes
4answers
344 views

Problem with WhenEvent

I am trying to add a time dependent fraction to a parameter in NDSolve, i.e. when 10 < t< 20, add ...
13
votes
2answers
1k views

Basins of Attraction

How does one shade the basin(s) of attraction of a phase plot in Mathematica? I have been trying to do this using the system $$\begin{align*} \dot x &= y\\ \dot y &= -9\sin(x) - 0.20y ...
3
votes
1answer
615 views

NDSolve for a large system of simple ODEs

I am solving a system of many (more than 100) ODEs. It is the kind of standard rate equation encountered in semiconductor physics. Here is the system: ...
4
votes
1answer
232 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 ...
0
votes
2answers
470 views

NDSolve solution for driven damped pendulum diverges

I want to solve numerically for the system of the driven damped pendulum using Mathematica. This is the second-order nonlinear equation \begin{equation} \ddot{x} + 2 \beta \dot{x}+ \omega_0^2 \sin ...
3
votes
1answer
196 views

Distance between two functions satisfying a constraint

My problem is that I have two functions that are described as follows: ...
4
votes
1answer
307 views

Using a user defined NormFunction in FindFit or NDSolve

I would like to use a different norm instead of the 2-norm in FindFit (Mathematica 9). For example, instead of using $$\sqrt{\sum (x_{\mathrm{model}} - ...
2
votes
0answers
292 views

Conditional statements in intial conditions?

This is potentially a daft question, but I thought I'd ask it; I have some material free to diffuse in a boundary between rn and ro; I've been able to get it working nicely for neumann type boundary ...
2
votes
1answer
395 views

Non linear equation phase space

As a supplementary to my question solution of differential equation I post a new question of how is it possible to make a Table that has elements the solutions of a non linear differential equation, ...
3
votes
2answers
438 views

Animating the Lorenz Equations

I am trying to use the Animate command to vary a parameter of the Lorenz Equations in 3-D phase space and I'm not having much luck. The equations are: ...
0
votes
1answer
196 views

solution of differential equation

I have the following code that gives you a phase portrait of a 2d system and I can't understand what means the 3rd and 4th line (sol1 and sol2). ...
1
vote
2answers
987 views

How does one specify Neumann conditions for NDSolve?

I have a series of functions defined in my notebook, and then want to use this to solve a diffusion-reaction type equation. At the moment, something like this works: ...
4
votes
2answers
222 views

Problem with adding vector to symbolic function (for NDSolve)

I'm trying to set up a system of differential equations for passing to NDSolve. Note that my initial conditions are vector valued so Mathematica should know that ...
0
votes
0answers
308 views

DSolve::overdet for system of linear PDEs

I would like to resolve symbolically the following equation: ...
0
votes
2answers
302 views

Problems with NDSolve and stiffness

I am trying to solve an ODE in chemical kinetics: $$\begin{align*} \frac{\mathrm d[x]}{\mathrm dt} &= -k_1 [x][y]\\ \frac{\mathrm d[y]}{\mathrm dt} &= k_1 [x][y] - k_3[y] \end{align*}$$ My ...
17
votes
1answer
1k views

Optimizing a Numerical Laplace Equation Solver

Laplace's Equation is an equation on a scalar in which, given the value of the scalar on the boundaries (the boundary conditions), one can determine the value of the scalar at any point in the region ...
2
votes
1answer
224 views

Plot differential equation system in a complex way

Based on this differential equation system: $$\begin{align*} \dot{x}&=f(x,y)\\ \dot{y}&=g(x,y) \end{align*}$$ where $$\begin{align*} f(x, y)&=x^2+y^2-25\\ g(x, y)&=x^2-y^2-7 ...
1
vote
1answer
93 views

Using Manipulate Feature for Two ODE's

So I have not been able to find any examples of the Manipulate feature for two ODE's. I would like to plot a graph of x[t] vs. y[t] and manipulate the initial conditions, v and theta. Thank you very ...
3
votes
1answer
99 views

How could I find the singular solutions of an ODE?

Starting with the equation $$y^{\prime\prime}x^2={y^\prime}^2$$ I could only get the general solution using DSolve: ...
5
votes
2answers
3k views

Solving a system of ODEs with the Runge-Kutta method

I´m trying to solve a system of ODEs using a fourth-order Runge-Kutta method. I have to recreate certain results to obtain my degree. But I'm a beginner at Mathematica programming and with the ...
2
votes
2answers
495 views

How to remove a singularity with WhenEvent

Bellow I have a differential equation which hits a singularity at low values of t. What I want to do is somehow utilize the WhenEvent command in order to replace ...
0
votes
2answers
251 views

characteristic polynomial based on differential equation

I have this differential equation: $$\ddot{x}-\frac{1}{6} \dot{x} - \frac{1}{6}x = e^t$$ When I DSolve it looks like this: ...
2
votes
1answer
374 views

NDSolve complains about missing derivatives of dependent variables in Mathematica 9

In Mathematica 8 NDSolve[{x[t] == 1, x[0] == 1}, x[t], {t, 0, 10}] solves fine and returns ...
1
vote
2answers
558 views

Solve Differential equation system

I've tried to solve this differential equation system, buy without any luck. This is my code: ...
1
vote
2answers
558 views

How can I use FindRoot on an expression from NDSolve?

I have a second order ODE that I can only solve numerically using NDSolve, but I then need to use the solution in FindRoot and am running into errors. A simplified but analogous problem is the ...
4
votes
1answer
326 views

Create Euler equation

I've tried to make some research, but without any luck. How do I setup the Euler equation for this in Mathematica?: $ \text{Min} \int_0^1\left(2x^2+ \left(4t-5 e^{r \, t} \right) x \, \dot{x} + ...
4
votes
2answers
521 views

WhenEvent in NDSolve

How come this doesn't work as I intended? ...
2
votes
1answer
598 views

Tutorial for basic numerical methods for PDEs

I'm afraid this is probably not going to be a "good" question, but I'd like to use Mathematica to learn about basic numerical schemes for solving pdes. For example, I'd like to compute the solution of ...
2
votes
2answers
667 views

Putting NDSolve into ParametricPlot

I am having issues using Manipulate to plot the (numeric) solution to an ODE for different parameter values. I have a code that has several stages, which seem to ...
5
votes
0answers
86 views

Modify NDSolve`StateData (if possible)

I am trying to solve a PDE that needs to be scaled constantly (refer to this). @andre suggests I modify NDSolve`StateData. Now, the problem is, I'm not used to ...
3
votes
2answers
627 views

NDSolve: Normalizing at every step

Suppose I have an transport equation with an initial conditions: ...
2
votes
2answers
375 views

BC for transport equation using NDSolve

First I can solve a transport equation with a source (Is it still called transport equation?) using DSolve. The form of the source serves only as an example. It can ...
4
votes
0answers
461 views

Kalman filter by hand

I am now learning the Kalman filter and wants to implement it by hand to understand it better. To be specific I want to first simulate a sequence of data by $$ \dot x=Ax+Bw\\ y=Cx+Dv,\\ ...