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

learn more… | top users | synonyms

0
votes
1answer
360 views

NDSolve example - analytical vs numerical solution. How to specify initial conditions?

So, I have the following equation: y[t]^-3 == w^2 y[t]/t^2 + y''[t] where w^2 = (t0 k0)^2. Analytic solution is easy to ...
2
votes
1answer
158 views

The output is the same as Input when I add the boundary conditions to a PDE

I am trying to solve a PDE in the first order with specific boundary conditions. When I solve use DSolve without the boundary conditions, Mathematica gives me an answer in an arbitrary function. When ...
2
votes
2answers
536 views

How to visualize slope fields of differential equations without vectors?

I'm looking to visualize slope fields of differential equations for my differential equations course. Every example I see draws them as vectors, adding unnecessary "arrows" that, to me, are visually ...
0
votes
1answer
234 views

Initial and boundary value errors

NDSolve::ivone: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >> I keep getting this, ...
0
votes
1answer
114 views

Plotting the discrete solution to a PDE

So I went through all the grunt work of solving a PDE in discrete form for a research project. Now I have a Temperature solution as a function of time and space: $$ T_{i}^{n+1}=\left( \dfrac ...
0
votes
0answers
252 views

How to obtain differential equations of motion using Lagrangian dynamics?

I'm confused to find a set of differential equations of motion of a pair of masses, m1 and m2 joined by a spring of constant ...
0
votes
1answer
45 views

How do I pull from a data list for parameter values in a system of ODEs and then solve and plot?

I have a parameter set list and I would like to solve a system of ODEs multiple times using each parameter set in the list. Then I would like each set of solutions to be graphed on the same plot. ...
0
votes
0answers
137 views

Boundary Condition Problem with Green's Function

My temperature distribution looks like: Mean wire temperature is : To[x_] := 2 c1 Cosh[x a1] + a2 And it is continuous at two points. In positive part: ...
0
votes
0answers
240 views

Shooting method for solving 3rd Oder ODE with RK method

This is my 3rd Order IVP. D[y[x], {x, 3}] == (m/2)*((D[y[x], x])^2 - 1) - ((m + 1)/2)* y*(D[y[x], {x, 2}])^2. Initial conditions given are as follows ...
0
votes
3answers
427 views

Find an equations of motion using Euler Eqution [closed]

I am a completely new to Mathematica, so my question and code may look silly. I need to find a equation of motion of a point particle of mass m moving in a potential V(x) = A abs[x]^n. (n=1,2,3,4,5,6. ...
3
votes
1answer
180 views

NDSolve with varying PrecisionGoal and WorkingPrecision

Sometimes we need higher numerical precision to deal with large number cancellation in an equation. But if this cancellation happens only in a small (and known) parameter space, would it be possible ...
6
votes
2answers
708 views

StreamPlot for Bifurcation Diagram

When we do a StreamPlot, I want to show the bifurcation when $a = 0$ transitions to $a >0$, but do not see a better way to do this than the following. ...
2
votes
0answers
138 views

Internal Shooting Method of NDSolve in combination with NDSolve`Reinitialize?

To explain my problem, I am trying to extend the BVP problem example from the help that illustrates how to use the shooting method of NDSolve: ...
11
votes
3answers
983 views

Plot Matlab icon

I started to explore this on a whim and hasn't succeeded yet… Some introduction for the icon is found here but I can't understand it very well. (I admit that, though playing with ...
0
votes
1answer
121 views

Setting plot size within vector; dynamic slider (two part question)

I have a question about the size of a plot in mathematica. I'm working on some differential equations (a simplified model of heat transfer in a building). I've programmed it so that you can set ...
0
votes
0answers
32 views

How to Invert a Multivariate Interpolating Function? [duplicate]

I used NSolve on a partial differential equation with boundary conditions to get a numerical solution that Mathematica says is of the form InterpolatingFunction. I then defined a function f(x,y) which ...
0
votes
1answer
236 views

Infinite expression 1/0.^(1/4) encountered in NDSolve

I am trying to solve very simple system of coupled differential equations using the NDSolve function, but I am getting ...
0
votes
0answers
308 views

How to apply Robin boundary condition in Mathematica

Robin condition is the boundary condition which combines the Dirichlet and Neumann condition at the same boundary. For example: At the boundary x = 0 to 2: I want to apply ...
0
votes
0answers
143 views

Maximum of NDSolve output. Problem with interpolating function

I solve a NonLinear PDE and get a solution (which for other reasons I put into a vector): SolVec1[1][[2]][x,t], where x and t are the indipendent variables. Now, I would like to get a distribution ...
0
votes
1answer
297 views

Using NDSolve for three variables as function of time

I want to be able to plot z, and r. Should I be using DSolve, NDSolve or something else? I've tried to clear it up a bit Thanks, Will ...
3
votes
1answer
348 views

Solving Rotational Equations of Motion

I'm trying to integrate the rotational equations of motion ...
10
votes
1answer
3k views

How to solve a system of partial differential equations?

Edit: since the upgrade to Mathematica 10, this problem seems solved I just want to solve a system of partial differential equations, for example: $$ \left\{ \begin{array}{l} ...
1
vote
1answer
255 views

Boundary condition is not specified on a single edge of the boundary of the domain

I am attempting to solve a PDE as prescribed in a paper I am reading; however, Mathematica doesn't seem to be happy with the way I am posing the problem. Im my case, r(t,100) is an approximation of ...
0
votes
1answer
191 views

Cannot get specific value from NDSolve (multiple functions)

I am trying to solve six connected differential equations. This is my code: ...
1
vote
1answer
296 views

Need help with solving a second order differential equation

I need help with solving this differential equation. ...
3
votes
1answer
316 views

Solving a constrained vector system with NDSolve

I'm trying to replicate the pendulum DAE example in the Documentation Center (example/ModelConstrainedSystemsAsDAEs) using Mathematica 9's vector support with NDSolve. So far I have: ...
1
vote
1answer
445 views

Use Euler method to solve differential equation

Use Euler's Method or the Modified Euler's to solve the differential equation ${dy/dt=y^2+t^2-1, y(-2)=-2}$ on $[- 2, 2]$. Take h = 0.2 (...
2
votes
1answer
156 views

Mathematica can't find constants for this differential equation

I am having problems solving this differential equation: diffeq = m x''[t] == -a E^(b*x'[t]); sol = DSolve[{diffeq, x[0] == 0, x'[0] == v0}, x[t], t] The output ...
1
vote
1answer
195 views

Partial differential equation with initial conditions

And so I want to solve the following equation, subject to these initial conditions: $\ u_{tt} - u_{xx} = 6u^5+(8+4a)u^3-(2+4a)u$ $\ u(0,x)=\tanh(x), u_t(0,x)=0$ When I use NDSolve to solve within ...
0
votes
0answers
130 views

How to solve a ParametricNDSolve issue when the system seems to be stiff?

I have a problem with ParametricNDSolve[]. Mathematica gives the warning that a stiff system is suspected. I have varied the methods but unfortunately I was not ...
5
votes
3answers
312 views

Kinetic Friction in Mathematica, weird behaviour

I found the behavoiur of Sign function weird in the code below. when $T=10$ ...
1
vote
1answer
230 views

Looping with NDSolve?

I have a series of PDE equations that are solved with NDSolve for certain variables $a$ and $b$ - Now, I want to see the output at a time $t$ as $a$ and $b$ change; so I was thinking of a loop ...
1
vote
0answers
205 views

Complicated condition for system of differential equation

I am trying to solve a series of nonlinear differential equation with complex condition as described by block diagram below. The left figure describes general concepts and the right figure describes ...
1
vote
1answer
357 views

How to use Compile with NDSolve function for large no of differential equations?

Matrix M[t] and and Hamiltonian of same order L^n x L^n. ...
4
votes
1answer
254 views

How to choose MaxStepFraction for optimal speed of NDSolve

I'm trying to use NDSolve to solve a 1D Schrodinger's equation, and it seems that MaxStepFraction has huge effect on the ...
0
votes
1answer
118 views

Problem with Plot of Solution for NDSolve [closed]

I'm trying to plot the solution of an equation using NDSolve. For some reason nothing shows up in the plot. I checked the output of the interpolating function and it doesn't look like there is ...
2
votes
3answers
249 views

Differential equation of a physical property which can not be below zero

A simple question but maybe also interesting for others. I have the simple differential equation: a'[t] == -r The quantity a has a physical meaning and can not ...
0
votes
1answer
141 views

Piecewise of different functions

You know, NDsolve coupled with Piecewise can be used to solve a series of discontinuous differential equations. But what if one of the function is different? For example: ...
1
vote
2answers
123 views

Eliminate complex answer to differential equation

I've tried the following: ...
0
votes
2answers
175 views

Asymptotic series

I need to solve the following problem. I have the following function: Erf[Sqrt[a x^2 + b y^2]]/Sqrt[a x^2 + b y^2], where x and y are variables and a and b ...
1
vote
2answers
178 views

Solving an ODE with parameters and conditions

I am trying to use Mathematica to solve a relatively simple ODE involving parameter(s). I would like to use a set of conditions to solve for the particular solution of the ODE. I understand how to ...
9
votes
0answers
155 views

Possible bug with FourierTransform linearity

Each component is easily transformed but the sum is not: FourierTransform[f''[x], x, k] FourierTransform[f'[x], x, k] ...
0
votes
0answers
54 views

Error in using EventLocator in NDSolve

I have a problem in using EventLocator in Mathematica 9. However, this error doesn't show up in Mathematica 8 on my labtop. My code is, ...
4
votes
2answers
815 views

Error entering equation in DSolve

I entered a command incorrectly as follows: DSolve[{y'[x]=y[x]},y[x],x] I am now experiencing: ...
0
votes
0answers
263 views

Unable to Solve Two-Point Boundary Value Problem

I'm trying to solve the equation -u''[x] + ((x - k)^2 - en[x]) u[x] == 0 using the boundary conditions ...
0
votes
0answers
169 views

Awkward Two-Point Boundary Value ODE

I'm trying to solve the following differential equation: -u''(x) + ((x-k)^2 -en)u(x)=0 with boundary conditions u(0)=0 and u(infinity)=0. Implementing this is Mathematica has led me to very cumbersome ...
10
votes
3answers
1k views

help to plot Poincare section for double pendulum

I am reading a book about classical mechanics. In the chapter about chaos, it gives the simplified and scaled equations for double pendulum as $$ \frac{d}{dt}\left[ \begin{matrix} \alpha \\[3mm] ...
0
votes
0answers
165 views

Differential equation with random variable

How can I derive analytically or compute numerically the solution to following differential equation $$ dy/dt = y\cdot X\cdot (y\cdot X - g(y,X))\cdot X $$ where X is a random variable (e.g. from a ...
1
vote
1answer
372 views

Fitting data using a differential equation

I have data generated from two functions given below. How can I go about finding a fit of the form: y'[x] == -(a + b/(c + d y[x] + e F[x] )) where a,b,c,d,e are ...
0
votes
1answer
247 views

Animation of 2 Differential Equations - 1 Independent Variable

I have effectively 1 differential equation that had to be broken up into 2 (max number of steps reached). I have gotten the solutions for both using NDSolve and have plotted each together. Now, I am ...