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

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2
votes
0answers
100 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
99 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
37 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
95 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
66 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
50 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
95 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
53 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
155 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
82 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
94 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
180 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
71 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
37 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
132 views

ParametricNDSolve and plotting problem

I have a problem with ParametricNDSolve: ...
3
votes
1answer
174 views

Combining Gravity Turn and Orbit Models

I have a mathematical model for the motion of an orbiting spacecraft about Earth: ...
0
votes
2answers
54 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
vote
0answers
60 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
26 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
40 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
vote
0answers
46 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
97 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 ...
0
votes
1answer
112 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 ...
0
votes
0answers
39 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
130 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
89 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? ...
6
votes
1answer
238 views

Poisson PDE using FDM in Mathematica

The problem modeled by the Poisson PDE is related to the torsion of prismatic beams and I use the Finite Differences Method. When I use Mathematica to solve it using a quadratic mesh it is working ...
1
vote
1answer
54 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 ...
0
votes
0answers
33 views

How to tell NDSolve to ignore small values in choosing step size

I have a very large system of first order differential equations, which can be written (on paper) as dX/dt=F(X), where X is a vector and F is a vector function. All elements of X are strictly positive ...
0
votes
2answers
102 views

recursive depth of 1024 exceeded [closed]

Can some tell me what is wrong in the following code. ...
1
vote
1answer
111 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
65 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 ...
2
votes
0answers
56 views

Can't find the limit of this complicated expression

Here is the limit I am trying to calculate ...
1
vote
2answers
53 views

Solving a differential equation with NSolve and ploting 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 (wich I might want to manipulate too). I want to plot the graph ...
0
votes
0answers
59 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 ...
1
vote
2answers
134 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
74 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
162 views

Problem with Neumann condition in quarter disc

So I'm following the available examples in version 10 for FEM, The plane stress operator is shown as this ...
0
votes
1answer
68 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
195 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
119 views

DSolve returning { } when given my ODE

Why does this code return {}? ...
2
votes
1answer
126 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 $w$ = ...
1
vote
0answers
70 views

Numerical solution to two non-linear coupled differential equations [closed]

I am trying to solve two differential equations representing the position of an object in space. I have specified arbitrary initial conditions. ...
4
votes
1answer
107 views

Using NDSolve to solve a system of coupled PDEs

I am trying to solve the Gross-Neveu model in one dimension for a specific soliton initial condition. I am trying ...
5
votes
2answers
202 views

Simplifying general solutions of differential equations (driven harmonic oscillator)

Solving general differential equations in Mathematica usually leads to somewhat unsightly results. As an example, consider the solution of the driven, damped harmonic oscillator: ...
2
votes
1answer
84 views

StateResponse is non-deterministic

I observed non-deterministic behaviour in StateResponse. Let's look at an example. ...
5
votes
1answer
101 views

Drawing disk with coordinates from NDSolve

I have simple Manipulation expression, but continuously getting error Coordinate {x[0.], y[0.]} should be a pair of numbers, or a Scaled or Offset form. I assume that something is wrong with ...
0
votes
0answers
47 views

Why NDSolve With Orthogonal-Projection Method On Orr-Sommerfeld Equation Does Not Work(?)

I am attempting to solve the Orr-Sommerfeld equation for plane Poiseuille flow with the Orthogonal Projection method within NDSolve. The Orr-Sommerfeld equation is (a "stiff" problem); $\psi''''(x) ...
1
vote
1answer
32 views

Error following a variable in an ODE [closed]

I am trying to solve a 4th order differential equation and this is my code thus far ...