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

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4
votes
1answer
349 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
342 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
485 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
583 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
208 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). ...
3
votes
2answers
1k 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
248 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
411 views

DSolve::overdet for system of linear PDEs

I would like to resolve symbolically the following equation: ...
0
votes
2answers
353 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
242 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
96 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
108 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: ...
7
votes
2answers
4k 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
633 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
317 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
422 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
798 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
743 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
390 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
683 views

WhenEvent in NDSolve

How come this doesn't work as I intended? ...
2
votes
1answer
708 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
795 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
94 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
731 views

NDSolve: Normalizing at every step

Suppose I have an transport equation with an initial conditions: ...
3
votes
2answers
471 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
525 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,\\ ...
2
votes
0answers
386 views

differential equations with implicit functions

I have an ordinary differential equation that contains coefficient functions that depend implicitly on the independent variable via an algebraic equation. I am trying to go ahead and use NSolve to ...
4
votes
1answer
2k views

Is it possible to impose “Assumptions” in DSolve or equivalent? (differential equation solving)

When DSolve tries to solve differential equations, it is sometimes not smart enough to generate conditions according to different possible value of parameters. ...
1
vote
1answer
706 views

Finding numerical/analytic solution to a derivative

Consider the following system of equations, with 11 dependent variables: ...
0
votes
0answers
1k views

DSolve fails to solve second order PDE

I have a very simple example of a second order PDE: eqn = D[u[x, y], x, y] + u[x, y] == 0; sol = DSolve[eqn, u, {x, y}] and Mathematica cannot solve it! What is ...
5
votes
1answer
644 views

NestList and Euler's method

I am new to mathematica and so just experimenting with various programming constructs. Recently have been looking at NestList and how I could use this to implement ...
3
votes
1answer
1k views

NDSolve does not respond

For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
0
votes
2answers
705 views

How can I suppress message “… cannot be used as function”?

I'd really appreciate your help. The code gives me a solution, but in the end it says it cannot be used as function, which is not true. Script: ...
0
votes
1answer
193 views

Solving a differential equation for a variable in a function

This may sound like a very trivial question, but I need to solve a differential equation as follows: ...
0
votes
1answer
886 views

Steady states and eigenvalues for a non-linear system:

I am trying to understand a non-linear system of equations, and find their steady states and dynamics. I am noob to understanding Mathematica (I am using version 6, but I have access to the latest ...
1
vote
1answer
598 views

Problem using NDSolve

This might be some simple mistake, but I am running out of ideas. I am trying to fit an ODE system to some data. This error keeps appearing NDSolve::nlnum: "The function value {0.299812 - ...
12
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 ...
2
votes
1answer
358 views

ParametricPlot3D doesn't appear

Here I have one simple system solvable with NDSolve. I don't know why ParametricPlot3D doesn't present trajectory in space. I have solutions for x[t], y[t] and z[t] ...
0
votes
1answer
412 views

Applying l'Hôpital's Rule to NDSolve with Piecewise Function

OK, so I've been working on this problem for over a week and it's driving me crazy. I'm trying to solve a system of two differential equations in $x(t)$ and $y(t)$ using a "time-elimination method," ...
4
votes
1answer
116 views

How can I highlight the vanishing-partials in an interactive 3D plot?

I am using Manipulate and Plot3D to plot a function with two real variables and two extra parameters. ...
1
vote
2answers
909 views

Weird NDSolve behavior with Piecewise (MMA9)

NDSolve in Mathematica 9.0.0 (MacOS) is behaving strangely with a piecewise right hand side. The following code (a simplified version of my real problem): ...
1
vote
1answer
797 views

How to calculate a gradient at x=0?

I am solving a second order differential equation for n[x]. I solved it with both DSolve and NDSolve. A plot of n as a function of x looks great. Than I want to calculate a gradient of n[x] at a ...
1
vote
1answer
312 views

Troubleshooting an NDSolve::ndfdmc error message

Τhe following code ...
1
vote
2answers
631 views
2
votes
1answer
182 views

Solving a system consisting of an ODE and a non-differential equation

I would like to solve the following system of equations: y'[t] == x[t]*y[t] - x[t]; 10 == x[t]*y[t]/(x[t] + y[t]) + x[t]/(x[t] + y[t]^2) Is there any way to ...
2
votes
2answers
415 views

Solving and plotting ODEs while varying one of the initial conditions

How can I vary an initial condition in the numerical solution of a system of ODEs and then make a 3D plot of the solution space with that condition as one of the variables. ...
16
votes
1answer
2k views

2D Heat equation: inconsistent boundary and initial conditions

I'm attempting to use NDSolve on a 2D boundary value problem with initial conditions. Upon running my code, I get the following message: "NDSolve::ibcinc: Warning: Boundary and initial conditions are ...
6
votes
2answers
487 views

Symmetry-finding packages

Where can I find the most up-to-date or whatever you consider to be the most useful symmetry-finding package for differential equations? I do not intend to restrict to, but would like to include ...