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

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1
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1answer
163 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 ...
1
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0answers
147 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
174 views

Turning arrowheads off

My thinking was that Arrowheads[0] would turn off the arrowheads. ...
4
votes
1answer
136 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
114 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
373 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
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0answers
49 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: ...
4
votes
1answer
129 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 ...
2
votes
0answers
495 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
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2answers
172 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
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2answers
348 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
280 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} ...
3
votes
1answer
158 views

Troubles with FindFit for ODE

I need to use FindFit for ODE with arbitary number of parameters. This code (from documentation) works: ...
1
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2answers
66 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
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1answer
167 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 ...
1
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0answers
193 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
269 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. ...
3
votes
1answer
193 views

Hermite method in Mathematica

When I solve the example below, in the results it is mentioned that Mathematica 10 has used the Hermite method. I cannot find anything about this in the Mathematica documentation. Is there nothing ...
1
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1answer
116 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
349 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
162 views

Evaluate function defined by DifferentialRoot

I have the following sequence of rationals that I want to find the generating function of: ...
2
votes
2answers
237 views

ParametricNDSolve and plotting problem

I have a problem with ParametricNDSolve: ...
4
votes
1answer
972 views

Combining Gravity Turn and Orbit Models

I have a mathematical model for the motion of an orbiting spacecraft about Earth: ...
0
votes
2answers
97 views

Derivative in function form

I have a function in mathematica defined as b[n_, x_] := x^n/n!/\!\(\*UnderoverscriptBox[\(\[Sum]\), \(k = n\), \(\[Infinity]\)]\*FractionBox[\(x^k\), \(k!\)]\) ...
1
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0answers
83 views

Updating procedural fitting algorithm to more efficient style?

For some time now, I have used this procedural programming approach to fit data in my research that is too cumbersome for the built in Mathematica functions. (Although this simple example works fine ...
0
votes
0answers
30 views

Identification of a parameter in a first order differential equation [duplicate]

I wan't to identify a parameter in a first oder differential equation. My goal is proof of the calculation principle i use. First I calculate a response where the paramater is set to 0.3. Later this ...
1
vote
1answer
96 views

NDSolve with WhenEvent, resetting system for a prolonged period

I am currently working on a complex system where I would like to (for the lack of a better description) reset (part) of the system for a certain period. Say I five ODE's: ...
1
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0answers
98 views

A Stupid Question Maybe - EigenNDSolve

I would like to find out how accurate and how useful the chebyshev (collocation?) method is in finding many eigenvalues to a second-order ODE in one go. Specifically, I used the Mathematica package ...
5
votes
2answers
159 views

How to add (energy) constraint when using NDSolve to Equation of Motion

To simplify my problem, I will try and solve the Equation of Motion for a particle in a 1D Harmonic Potential. energy[x_, p_, m_, ω_] := p^2/(2 m) + (m ω^2)/2 x^2 ...
1
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1answer
116 views

Fit to inverse function

I am trying to fit my data to an inverse function from solving a DGL: ...
0
votes
1answer
76 views

Why does DSolve fail here?

I have the following differential equation: a*L'[t] == 40000*L[t]^(-3/2) - 1.4 - extf I want to fit the solution to data in order to acquire a. I tried DSolve ...
0
votes
1answer
118 views

Tough Calculation, novice mathematica user

I have an equation, that I've been calling $b_N(x)$ that satisfies the following identity: $$-Nb_N(x)^2=(x-N)b_N(x)+xb_N'(x)$$ where $b_N'(x)$ is the first derivative. I take the derivative then of ...
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0answers
204 views

NDSolve error message: Cannot find starting value for the variable y'

I'm attempting to solve a differential equation using NDSolve. This is the code: ...
2
votes
1answer
178 views

Analytic approximation of NDSOLVE

I have to solve the following differential equation L'[t] == L[t]^(-3/2) - 0.1 I tried DSolve: ...
0
votes
1answer
377 views

StreamPlot in a system x´ = f[x] + g[t] [closed]

StreamPlot can be used in the O.D.E system: x' = 2 x - 3 y + 3 t y' = 5 x + y - t How? ...
7
votes
1answer
514 views

Poisson PDE over a irregular region with FDM

The problem modeled by the Poisson PDE is related to the torsion of prismatic beams and I use the Finite Differences Method (FDM). I've managed to solve the equation over a rectangle region with ...
1
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1answer
126 views

Series expansion of InterpolatingFunction obtained from NDSolve

I am trying to obtain a series expansion of the numerical solution of a differential equation. I encounter difficulties going beyond first-order expansions which I believe might be due to my inability ...
1
vote
1answer
314 views

Solving system of differential equations using loops

I have $F$ system of differential equations. Out of those $F$ equations except for first and last I have general form for the remaining equations (say $ dP_{i}/dt)$. Let $dP_0/dt,dP_F/dt$ denotes the ...
1
vote
1answer
94 views

NDSolve with a constant

I have a simple differential equation like this s = NDSolve[{y'[x] == A y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}] where $A$ is a constant. Mathematica gives ...
7
votes
1answer
352 views

Second order differential equation with boundary conditions solving repeatedly

I want to solve a second order differential equation in the interval[-1:1], which does not have a analytic solution, \begin{eqnarray} y''(x) &=& k \phi^2(x)y(x) \\ \phi(x) &=& ...
2
votes
0answers
66 views

Can't find the limit of this complicated expression

Here is the limit I am trying to calculate ...
2
votes
3answers
137 views

Solving a differential equation with NDSolve and plotting it WITH the use of Manipulate

I want to solve, let's say, this differential equation: y'[x]=y[x]^n Given any initial condition (which I might want to manipulate too). I want to plot the ...
0
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0answers
205 views

How to solve system of non linear Differential Equations with 1 independent variable and 3 dependent variables?

I have been trying to solve this system of differential equations using mathematica. $$F(t) B''(t)+B'(t) F'(t)+B(t) F''(t)=0,\\ F(t) A''(t)+A'(t) F'(t)+A(t) F''(t)=0, \\ B(t) A'(t)+A(t) B'(t)=0$$ Here ...
2
votes
2answers
205 views

Solving Differential Algebraic Equations as BVP

I am trying to solve a set of DAEs. \begin{equation} -4 \nu (\lambda(s))^{(-1 - 4 \nu)} \theta'(s) \lambda'(s) + (\lambda(s))^{(-4 \nu)} \theta''(s) = -\alpha_y \cos\theta(s) + \alpha_x ...
0
votes
1answer
239 views

NDSolveValue with a multiple variable equation

I'm trying to plot this equation of motion for a pendulum with a periodically applied torque for 20 cycles, where b, m, L, g are given constant values. ...
7
votes
1answer
278 views

Problem with Neumann condition in quarter disc

Bug introduced in 10.0 and fixed in 10.2 So I'm following the available examples in version 10 for FEM, The plane stress operator is shown as this ...
1
vote
1answer
294 views

How can I stop the integration of NDSolve with a condition?

I try to solve a partial differential equation by NDSolve. At some point, I want to stop the integrating by a condition that compares the min value of the function ...
3
votes
3answers
343 views

Higher-order, nonlinear differential equation with Initial Values

I tried to solve for an non-Hookean spring's motion, but the output from Mathematica is weird. It seems that there is inverse functions involved. ...
2
votes
2answers
122 views

DSolve returning { } when given my ODE

Why does this code return {}? ...
3
votes
1answer
260 views

Problems with NDSolve and partial differential equations of several variables

Suppose we have the following partial differential equation: $$ 0 = \frac{ \partial w }{ \partial \tau } + \left( w + \sqrt{ h + \beta } \right) \frac{ \partial h }{ \partial \chi } $$ where $w$ = ...