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
41 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
48 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
98 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
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0answers
46 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
96 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
249 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
60 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
34 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
161 views

recursive depth of 1024 exceeded [closed]

Can some tell me what is wrong in the following code. ...
1
vote
1answer
120 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
66 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
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0answers
57 views

Can't find the limit of this complicated expression

Here is the limit I am trying to calculate ...
1
vote
2answers
58 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
67 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
136 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
87 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
175 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
73 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
203 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
120 views

DSolve returning { } when given my ODE

Why does this code return {}? ...
2
votes
1answer
137 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
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0answers
74 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
120 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
212 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
85 views

StateResponse is non-deterministic

I observed non-deterministic behaviour in StateResponse. Let's look at an example. ...
5
votes
1answer
105 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
49 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 ...
0
votes
0answers
48 views

Resources about Geodynamics

I'm about to start a small project on numerical geodynamic. If possible, I whish to handle the computational work in Mathematica. The project will be small but probably not so small I can do all by ...
0
votes
0answers
189 views

Poincare Section of an Hamiltonian

I'm in desire to plot the Poincare Section of a differential equation defined by a hamiltonian system. The hamiltonian is as follow: ...
14
votes
1answer
534 views

Has this implementation of FDM touched the speed limit of Mathematica?

Still, I'll use the implementation of the 1D FDTD method (you can simply understand it as a kind of explicit finite difference scheme for the Maxwell's equation) as the example. Just for completeness, ...
0
votes
1answer
101 views

Attempt to solve for Differential Equation - Acc, Vel, Pos in (x,y,z) [closed]

In the problem I'm working on, there is a tennis ball that is subjected to a headwind, tailwind, and crosswind. I am trying to use NDSolve in order solve for the position functions and to eventually ...
0
votes
1answer
78 views

Formulating a second boundary condition to get an alternative solution to a ODE [closed]

I have the ODE $c'(t) = t^2c^3$ with the initial condition $c(1) = 20$. The differential equation $c'(t) = t^2c^3$ (without boundary conditions) has two branch solutions. I want to formulate a new ...
1
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0answers
92 views

Taking a derivative, then squaring a two dimensional numerical function

Context I am interested in first finding an interpolating function of the solution to the linearly damped wave equation. Here is the solution to the LDWE with smooth square inital function : ...
0
votes
1answer
61 views

Plotting a solution of DSolve

I am trying to plot a solution of a differential equation system. This is what I have: ...
1
vote
1answer
98 views

Mathematica doesn't know the answer to this differential equation system

I am having some trouble with solving a somewhat heavy differential equation system, which is consisted of 10 variables and other abstract parameters as follows: ...
0
votes
0answers
36 views

Finding derivatives in a differential equation system

I have a differential equation system with 10 variables whose functional forms are: $\lambda_R = \alpha_0 + \alpha_1 P_R$ $E_R = \theta_0 + \theta_1 P_R$ $\lambda_X = \beta_0 + \beta_1 P_X$ $L_D = ...
1
vote
1answer
58 views

Code for time derivative or time differential equation

I have three variables $X, Y, Z$ whose functional form is the following (I also have a function for $Z$ which is somewhat complicated but is not essential for my question here; so it is omitted.): ...
1
vote
1answer
115 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
2
votes
0answers
92 views

Puzzling NDSolve[] behavior for PDE (smooth solution, inconsistent with boundary conditions)

Consider the following: NDSolve[{D[z[x, y], x, x] + D[z[x, y], y, y] == 0, z[x, 0] == Sin[x], z[0, y] == Cos[y]}, z[x, y], x, y] {{z[x, y] -> ...
0
votes
0answers
66 views

NDSolve with mixed boundary conditions

I am trying to solve a spherical Laplace equation subjected to Neumann boundary conditions in the lower half ($θ < π/2$) and constant potential in the other half (say, $f(R,\, θ) = 0,\, {\rm if}\ θ ...
2
votes
1answer
229 views

ParametricNDSolve KKT Constraint Directly

I am trying to directly solve for an optimal control using Pontryagin Maximum, where H is the Hamiltonian, in the presence of a KKT constraint. The constraint is ignored. I am wondering if a direct ...
1
vote
1answer
158 views

Smoothing a single rectangular pulse in NDSolve

Hello I am interested in smoothing out the sharp edges of a single rectangular wave centered at the origin. I am looking for a smooth function that looks almost exactly the same as the square wave ...
3
votes
0answers
71 views

Increasing MaxPoints in NDSolve results in memory issue

I am interested in increasing "MaxPoints" in NDSolve's "MethodOfLines" in attempt to increase the resolution of the plot of the solution of linearly damped wave equation with transparent boundary ...
2
votes
0answers
204 views

How to solve a nonlinear coupled PDE with initial and some boundary values

I would like to solve the following nonlinear coupled PDE with a mix of initial conditions and boundary values: ...
0
votes
0answers
68 views

No solution with DSOLVE

I have been trying to solve the following system of ODEs: \begin{eqnarray} ...
0
votes
1answer
69 views

Substitution of a function in a differential equation

Suppose we have a differential equation as follows: g[t_] := t/2 m[t_] := t/3 A[t_] := {{g[t], 1}, {1, m[t]}} p'[t] == A[t]. p[t], p[0] == {1, 0} ...
3
votes
5answers
239 views

Output is Input for a Differential with Sign?

Here's the problem: For one of my classes, we're supposed to use Mathematica to solve the equation y''=y-b*y' for a variety of b values and specified boundary conditions and plot the outputs. There I ...