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

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5
votes
1answer
100 views

Solve a differential equation with an integral inside?

I am trying to solve this differential equation in Mathematica: y'[t]+integral from 0 to t of y[x]dx =e^(-t) where y[0]=0. Is this possible?
9
votes
2answers
369 views

Water Hammer - Numerically solving system of PDEs

I'm trying to use Mathematica to solve the water hammer effect. ...
0
votes
1answer
82 views

Parametric Plotting

I am trying to make a parametric plot of the x and y displacements of a vibration problem. When trying to plot the parametric curve won't show up.
0
votes
0answers
147 views

Time-dependent mesh deformation

I want to display the result of a deformation with a mesh, but I solved the deformation with a time dependency. So I have two functions: uxsol[t,x,y] and ...
3
votes
1answer
139 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
77 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
147 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
73 views

Maximising solutions of NDSolve [duplicate]

I have the following system of differential equations ...
0
votes
0answers
77 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
39 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
119 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
64 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
70 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
56 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
95 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
112 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 ...
0
votes
1answer
56 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
221 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
88 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 ...
5
votes
3answers
252 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
69 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
193 views

NDSolve solution does not satisfy boundary conditions

I am trying to solve a 1st order non-linear ODE ...
1
vote
0answers
109 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
vote
0answers
69 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
63 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
71 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
99 views

Why is my output equal to my input?

I tried to solve a system of differential equations with the code below: ...
2
votes
0answers
121 views

Volterra integral equation

I have to find an approximate numerical solution for the equation $$ F(x) - \lambda \int\limits_1^{x} \text{d}s \;s^2 F(s) Z(x-s) = G(x) $$ $$Z(s) = (\psi''(1-2\ h\ i\ s)- 0.5 \psi''(1-2\ h\ i\ s))$$ ...
3
votes
2answers
147 views

Turning arrowheads off

My thinking was that Arrowheads[0] would turn off the arrowheads. ...
4
votes
1answer
121 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
vote
0answers
64 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
276 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
44 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
79 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
73 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
157 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
115 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]: ...
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
113 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
74 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
34 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
53 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
107 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
72 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
207 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
87 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
97 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
216 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
86 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
69 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: ...