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

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3
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1answer
176 views

Introduction to Vectors and NDSolve

I want to use NDSolve for a complicated equation that contains vectors. I am still new to Mathematica, and have really enjoyed what I have learned thus far. Concerning this question, I have already ...
2
votes
2answers
157 views

How to generate pure function solution using NDSolve

Suppose i have an equation NDSolve[{ca'[t]== -0.1*ca[t]*cb[t], cb'[t]== -0.1*2*ca[t]*cb[t], ca[0]== 10, cb[0]== 12},{ca,cb},{t,0,5}] how can i get the ...
2
votes
1answer
207 views

Problem solving a nonlinear differential equation with specific boundary conditions

I am trying to solve the following differential equation: DSolve[{y''[x] == A*B (y[x])^2, y'[0] == -B*C, y'[-D] == 0}, y[x], x] For my system, this ...
1
vote
1answer
89 views

Maximising solutions of NDSolve [duplicate]

I have the following system of differential equations ...
0
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0answers
106 views

Boundary value problem: complicated functionals

I am trying to solve a non-linear boundary value problem where the differential equation is a convoluted function of the variable I am trying to solve for. I have attached the code defining the ...
0
votes
0answers
46 views

Troubles with FindFit for ODE (elaboration)

I have asked a question Troubles with FindFit for ODE and get a good-working answer from @belisarius. Nevertheless I need to clarify is it possible to define the same model with ...
3
votes
0answers
167 views

Fractals or other patterns in the quadruple linked pendulum

This will seem like a physics question, but I'm looking for something to do in Mathematica specifically. I've successfully modeled a quadruple linked pendulum by setting up the ODEs and solving them ...
0
votes
0answers
92 views

Plotting Poincare sections for a pendulum

Now before you direct me to this page, I'll start by saying that I'm not really using Hamiltonian mechanics to do this problem. I've already done the Lagrangian and I have solutions for both angles. I ...
2
votes
1answer
105 views

Using NDSolve on a vector-valued PDE

I would like to use NDSolve to evaluate a PDE involving a vector valued function. For instance, I'm looking for something like a heat equation with vector-valued ...
0
votes
1answer
63 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 ...
1
vote
3answers
133 views

Difficulty understanding Inverse functions are being used by Solve

I am still having difficulty with the differential equation $$\frac{dy}{dt}=y^2-y,\quad y(0)=2$$ Consider: ...
2
votes
1answer
193 views

2 DOF Spring Mass Damper with NDsolve and Equation of Motion in Matrix Form

I'll preface this with the fact that I have no idea what I'm doing. I'm new to Mathematica, I've only used it to solve simple ODEs with NDsolve. I'm trying to solve ...
4
votes
1answer
271 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
0
votes
1answer
139 views

How to put constraints on NDSolve[] solution

Assumed the following example of double pendulum by Thison (Answered by Jens): Animation of double pendulum Imagine that in the given animation(i.e. http://i.stack.imgur.com/p4TgL.gif ), the second ...
2
votes
3answers
247 views

Mathematica won't plot the a function that is solved from NDSolve

I have used NDSolve to solve for a function (an angle of a triple pendulum), and now I wish to plot the derivative of that function (the angular velocity). ...
0
votes
1answer
96 views

Misunderstanding of Function Notation

I have: sol = DSolve[{y'[t] == y[t]^2 - y[t], y[0] == c}, y[t], t]; y[t_, c_] := y[t] /. First[sol]; Then: y[t,c] Produces ...
0
votes
1answer
59 views

DSolve for first order nonlinear equation is solution numerical or analytical?

Hi I'm new to mathematica so I may have a somewhat trivial question. my code below solves and plots the results of a first order nonlinear ODE. The solutions mathematica gives me contains & and #1 ...
5
votes
3answers
350 views

Numerically Simulating a Simple Differential Equation: RC Circuit

I need to learn to simulate a differential equation in Mathematica. The differential equation that I need to simulate is complicated, without an analytical solution. However, I am brand new to ...
2
votes
1answer
111 views

Breaking out of NDSolve

I am solving a coupled set of differential equations with NDSolve for 6 unknown functions of time. At a certain point in time, the system hits a singular point where the potential governing the ...
2
votes
2answers
297 views

NDSolve solution does not satisfy boundary conditions

I am trying to solve a 1st order non-linear ODE ...
1
vote
0answers
153 views

Plotting phase portrait from NDSolve (i.e., must plot x'[x], where $x=x(t)$)

I'm doing a double pendulum system and I wish to plot the phase portraits for each angle. I've successfully used NDSolve to solve for each of the angles. Let's just ...
1
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0answers
91 views

How to solve Fuzzy Differential Equations

How to solve Fuzzy Differential Equations using DSolve or NDSolve, Or Differential Equations with fuzzy number as initial conditions
1
vote
1answer
99 views

Plotting ODE solutions with two parameters

I have a system of two first-order ODEs with two parameters, a and b and I'm trying to plot the solution curve in the X-Y plane at a given initial condition for various parameter values. Can someone ...
0
votes
0answers
96 views

Solving PDE with conditions

I am new to Mathematica, so it maybe a silly question. So, I'm trying to solve the following PDE with Mathematica: $u=u(x,y)$ $\partial_x ^2 u-6\partial_x \partial_yu+9\partial_y^2u=x^2+y^2$ ...
1
vote
0answers
115 views

Why is my output equal to my input?

I tried to solve a system of differential equations with the code below: ...
3
votes
2answers
160 views

Turning arrowheads off

My thinking was that Arrowheads[0] would turn off the arrowheads. ...
4
votes
1answer
124 views

Can anyone help me to get the solution of this first order ODE?

$\ y'(x)=-\sqrt(y(x)^3)$ with initial condition $\ y(0)=-2$. In fact, this is an example here in page 3-4 ...
1
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0answers
80 views

Direction Field for an Ordinary Differential Equation [duplicate]

I have found links for plot the direction field of a differential equation. For example: How can I plot the direction field for a differential equation? And: Plotting the direction field of a ...
8
votes
1answer
344 views

How can I improve speed of code that generates an orbit plot?

I am attempting to generate an orbit for the "time 2 Pi map" of a forced damped pendulum. The example comes from page 57 in the Chaos text by Alligood,Sauer and Yorke, see Figure 2.7. The code ...
1
vote
0answers
48 views

The use of Evaluate in NDSolve and Plotting the answer [duplicate]

I am having a bit of hard time understanding the use of Evaluate when plotting the output of NDSolve. From the documentation, I enter: ...
3
votes
1answer
113 views

System of differential equations on a directed graph

I want to use Mathematica to model blood flow through a capillary network. The approach we are using is going to be to create a directed graph, and have a system of differential equations at each ...
1
vote
0answers
93 views

Maxwell propagator problem 2D [closed]

Hi folks I`m trying to turn certain matlab code to mathematica but for some reason it doesnt really want to do it could you please assist me a bit. Thanks The matlab code is as follows: ...
2
votes
0answers
322 views

NDSolve and strange “nonlinear coefficients problem”

I'm stuck solving the following problem. I defined two functions as follows: $$ \varphi(\lambda) = \frac{\left((\lambda-2)^2-1 \right)^2}{4}$$ $$ \gamma(\lambda) = \varepsilon^2 ...
2
votes
2answers
134 views

Can't use my own discontinuous coefficient within NDSolve

I want to evaluate the pendulum's motion with changing equilibrium state given by eqilValue[t]: ...
1
vote
2answers
210 views

DSolve bvlim error due to Boundary condition at infinity

I am solving an Ode using Mathematica that has boundary condition at infinity which is why Mathematica is showing error message. Please help to tackle this problem. ...
4
votes
1answer
225 views

Non-separable partial differential equation in polar coordinates

I'm trying to solve the Schroedinger equation in 2D for a system interacting via a dipole potential. This means, in effect, I'm trying to solve the nonlinear PDE $$ -\frac{1}{r} ...
0
votes
1answer
38 views

Coefficients of a DiffEq [closed]

I'm attempting a Do[] recursion on Coefficient[] with the end goal to use it to find the coefficients of an nth order diffeq. The following is a basic example of what I'm trying to do, subbing a ...
3
votes
1answer
134 views

Troubles with FindFit for ODE

I need to use FindFit for ODE with arbitary number of parameters. This code (from documentation) works: ...
0
votes
1answer
91 views

Plotting and Analysing derivatives of solution of differential equation [closed]

Using NDSolve I found the solution for the differential equation that governs the dynamics of a simple pendulum. How do I plot the derivatives of the solution? Also, I would like to find the ...
0
votes
0answers
37 views

Finding a specific number of eigenvalues in Mathematica

I'm trying to learn how to determine a specific number for eigenvalues for a transcendental equation. For example, ...
1
vote
2answers
62 views

Strange behavior of the Evaluate function

I am solving a system of differential equation whose unknown are saved under variable vec={C00,C01,C10,C11} and the solutions are saved under variable ...
1
vote
1answer
133 views

using Module in NDSolve

I am trying to solve a set of two wave equations where solution of first equation defines initial conditions for the second one. And I would like to use Module to define those equations as a function ...
0
votes
0answers
117 views

Help deciphering Neumann Value

Version 10 has an option for NDSolve called "NeumannValue" which is supposed to allow you to specify boundary conditions of the form $\vec{n} . (c \nabla u + \alpha u -\gamma) = g-q u$ but there is no ...
0
votes
1answer
241 views

Help solving the following non-linear differential equation

After spending several hours exploring different options, I still couldn't not figure out how to solve the following differential equations. Any suggestions would be highly appreciated. ...
2
votes
0answers
103 views

Hermite method in Mathematica

When I solve the example below, in the results it is mentioned that MMA 10 has used Hermite method. I cannot find anything about this in MMA documentation. Is there nothing about Hermite method ...
1
vote
1answer
106 views

Problem solving a differential equation

I want to solve the following differential equation: y''[x]+a*y[x]=-b*u[x], y[0]==0, y'[0]==0 for y(x). u[x] is a vector, ...
2
votes
2answers
277 views

ParametricPlot3D line not smooth

Multivariate parameters appear to present a jagged appearance of integrands (using default Runge-Kutta ODE integration intervals?) in ParametricPlot3D plotting on a single argument. Higher Mesh.. ...
2
votes
1answer
113 views

Evaluate function defined by DifferentialRoot

I have the following sequence of rationals that I want to find the generating function of: ...
0
votes
0answers
183 views

DSolve echoes input

I'm attempting to solve a set of coupled, non-linear ordinary differential equations using DSolve, but Mathematica simply echoes the code that I put in: ...
1
vote
2answers
212 views

ParametricNDSolve and plotting problem

I have a problem with ParametricNDSolve: ...