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

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5
votes
2answers
3k views

How to handle NDSolve::ndsz problem (singularity problem)

I have 2 second order differential equations (non-linear). The physics behind them is correct. I verified the equations many times. It is a solid pendulum with a mass-spring at the end of it. Now, ...
4
votes
2answers
141 views

Coordinate free differential forms package

I am looking for a package in Mathematica which can handle differential forms in a coordinate free manner. I am aware of several packages which do differential forms, but it seems that for all of them ...
1
vote
0answers
41 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: ...
14
votes
1answer
1k views

Animation of double pendulum

Sadly, I am a completely newbie. I am studying Physics and in our theoretical physics class we got the task to solve the double pendulum using Mathematica. We just got the program, but no introduction ...
1
vote
1answer
319 views

Solving a complex-valued differential equation with NDSolve

I am trying to solve $dx/dt=\sqrt{1+(ix)^{1.8}}$ for initial condition $x[0] =-0.9877 + i 0.1563$, where $x$ is a complex variable. I would like to plot the imaginary part of the solution versus the ...
2
votes
3answers
410 views

DSolve will not apply assumption m ∈ Integers

I am trying to solve a linear second order ODE using DSolve which involves an arbitrary integer m. ...
2
votes
0answers
97 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 ...
3
votes
1answer
71 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
65 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
2answers
97 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]: ...
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
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 ...
0
votes
1answer
65 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
1answer
628 views

how to solve second order nonlinear coupled differential equations using NDSolve with hyperbolic function

i have to solve some solitons scattering through this coupled equations. i need to get two different graph, but still the graph did not come out. and also the equations quite complicated containing ...
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
1answer
93 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
vote
2answers
49 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
2answers
128 views
6
votes
1answer
234 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 ...
0
votes
0answers
51 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 ...
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 ...
2
votes
2answers
179 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.. ...
1
vote
1answer
93 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
1answer
70 views

Evaluate function defined by DifferentialRoot

I have the following sequence of rationals that I want to find the generating function of: ...
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 ...
3
votes
1answer
171 views

Combining Gravity Turn and Orbit Models

I have a mathematical model for the motion of an orbiting spacecraft about Earth: ...
0
votes
0answers
36 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
0answers
59 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
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[\(x^k\), \(k!\)]\) ...
0
votes
0answers
238 views

Problem with Plot and ParametricNDSolve

This is my first question on this site, I hope it is written in an understandable way. Let's start. My aim is to plot a certain parametric region, with $x$ and $y$ coordinates given by the following ...
5
votes
2answers
96 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
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 ...
0
votes
0answers
68 views

Solving an ODE, where the coefficients are implicit functions of time, not in closed form [duplicate]

I have an ODE, say of the first order for simplicity, and of the form, $A.x'[t] =B$. The coefficients are functions of time and x[t], not in closed form. I can define the coefficients, $A$ and $B$, ...
1
vote
1answer
37 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 ...
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
111 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: ...
0
votes
1answer
86 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? ...
2
votes
1answer
125 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 $w$ = ...
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
95 views

recursive depth of 1024 exceeded [closed]

Can some tell me what is wrong in the following code. ...
1
vote
1answer
110 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
2
votes
1answer
123 views

Why do identifiers of the form ${\tt c}k\$nnn$ appear in the rules returned by my function?

I want to define a function, PolynomialInterpolation to find the coefficients of a polynomial interpolation function. My trial is as shown below: ...
1
vote
2answers
132 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 ...
1
vote
2answers
52 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
55 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 ...
9
votes
2answers
2k views

How to discretize a nonlinear PDE fast?

I wish to numerically solve the following PDE. Although there are some complete discussions for solving PDEs in tutorial/NDSolvePDE, there is no hint for the nonlinear case by discretization. Thus, I ...