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

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0
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1answer
133 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
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0answers
298 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
52 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
146 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
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0answers
300 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 ...
3
votes
1answer
229 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
767 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
1answer
216 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: ...
12
votes
3answers
1k 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
130 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
33 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
283 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
375 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
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0answers
163 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
356 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
393 views

Solving Rotational Equations of Motion

I'm trying to integrate the rotational equations of motion ...
10
votes
1answer
4k 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
302 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
240 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
310 views

Need help with solving a second order differential equation

I need help with solving this differential equation. ...
1
vote
1answer
225 views

Is it possible to give the closed-form of the stiffness matrix of triangular prism element?

Suppose the vertices of triangular prism are 1, 2, 3 (bottom triangle), 4, 5, 6 (top triangle), the coordinates of the vertices are $$ (x_i, y_i, z_i), i=1,2,3,4,5,6. $$ We can write the stiffness ...
0
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0answers
44 views

How to generate closed-form stiff matrix of triangular prism element by mathematica [duplicate]

We can generate closed-form stiff matrix of tetrahedron by mathematica: http://library.wolfram.com/infocenter/Articles/3233/ Can we also generate closed-form stiff matrix of triangular prism element ...
3
votes
1answer
361 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: ...
2
votes
1answer
552 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
164 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
270 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
156 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
326 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
263 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
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0answers
213 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 ...
2
votes
1answer
460 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
297 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
131 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
255 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
150 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
131 views

Eliminate complex answer to differential equation

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

Asymptotic series [duplicate]

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
192 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 ...
11
votes
0answers
186 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
57 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
1k 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
305 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
192 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
2k views

help to plot Poincaré 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
191 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
450 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
279 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 ...
1
vote
1answer
791 views

Error messages from NDSOlve

I am trying to solve a boundary value problem with NDSolve. The code is: ...
0
votes
0answers
110 views

DSolve not giving solution expected

I'm trying to solve the ODE $\frac{\partial M}{\partial \tau} = [ 4 c_3 N(\tau) + c_1 ] M(\tau),$ where $N(\tau) = \frac{q}{2 c_3} \frac{ 1 }{c_2 e^{2 q \tau} + 1} - \left ( \frac{ q + c_1}{4 c_3} ...
6
votes
1answer
183 views

Working with a system of differential equations that cannot be solved explicitly

I have to work a lot with three functions $\;o_1(t), o_2(t), o_3(t)\;$ that are solutions to the certain system of differential equations: ...