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
268 views

How to use Compile with NDSolve function for large no of differential equations?

Matrix M[t] and and Hamiltonian of same order L^n x L^n. ...
4
votes
1answer
224 views

How to choose MaxStepFraction for optimal speed of NDSolve

I'm trying to use NDSolve to solve a 1D Schrodinger's equation, and it seems that MaxStepFraction has huge effect on the ...
0
votes
1answer
106 views

Problem with Plot of Solution for NDSolve [closed]

I'm trying to plot the solution of an equation using NDSolve. For some reason nothing shows up in the plot. I checked the output of the interpolating function and it doesn't look like there is ...
2
votes
3answers
247 views

Differential equation of a physical property which can not be below zero

A simple question but maybe also interesting for others. I have the simple differential equation: a'[t] == -r The quantity a has a physical meaning and can not ...
0
votes
1answer
132 views

Piecewise of different functions

You know, NDsolve coupled with Piecewise can be used to solve a series of discontinuous differential equations. But what if one of the function is different? For example: ...
1
vote
2answers
110 views

Eliminate complex answer to differential equation

I've tried the following: ...
0
votes
2answers
156 views

Asymptotic series

I need to solve the following problem. I have the following function: Erf[Sqrt[a x^2 + b y^2]]/Sqrt[a x^2 + b y^2], where x and y are variables and a and b ...
1
vote
2answers
163 views

Solving an ODE with parameters and conditions

I am trying to use Mathematica to solve a relatively simple ODE involving parameter(s). I would like to use a set of conditions to solve for the particular solution of the ODE. I understand how to ...
8
votes
0answers
142 views

Possible bug with FourierTransform linearity

Each component is easily transformed but the sum is not: FourierTransform[f''[x], x, k] FourierTransform[f'[x], x, k] ...
0
votes
0answers
46 views

Error in using EventLocator in NDSolve

I have a problem in using EventLocator in Mathematica 9. However, this error doesn't show up in Mathematica 8 on my labtop. My code is, ...
4
votes
2answers
542 views

Error entering equation in DSolve

I entered a command incorrectly as follows: DSolve[{y'[x]=y[x]},y[x],x] I am now experiencing: ...
0
votes
0answers
202 views

Unable to Solve Two-Point Boundary Value Problem

I'm trying to solve the equation -u''[x] + ((x - k)^2 - en[x]) u[x] == 0 using the boundary conditions ...
0
votes
0answers
147 views

Awkward Two-Point Boundary Value ODE

I'm trying to solve the following differential equation: -u''(x) + ((x-k)^2 -en)u(x)=0 with boundary conditions u(0)=0 and u(infinity)=0. Implementing this is Mathematica has led me to very cumbersome ...
10
votes
3answers
1k views

help to plot Poincare section for double pendulum

I am reading a book about classical mechanics. In the chapter about chaos, it gives the simplified and scaled equations for double pendulum as $$ \frac{d}{dt}\left[ \begin{matrix} \alpha \\[3mm] ...
0
votes
0answers
126 views

Differential equation with random variable

How can I derive analytically or compute numerically the solution to following differential equation $$ dy/dt = y\cdot X\cdot (y\cdot X - g(y,X))\cdot X $$ where X is a random variable (e.g. from a ...
1
vote
1answer
316 views

Fitting data using a differential equation

I have data generated from two functions given below. How can I go about finding a fit of the form: y'[x] == -(a + b/(c + d y[x] + e F[x] )) where a,b,c,d,e are ...
0
votes
1answer
215 views

Animation of 2 Differential Equations - 1 Independent Variable

I have effectively 1 differential equation that had to be broken up into 2 (max number of steps reached). I have gotten the solutions for both using NDSolve and have plotted each together. Now, I am ...
1
vote
1answer
462 views

Error messages from NDSOlve

I am trying to solve a boundary value problem with NDSolve. The code is: ...
0
votes
0answers
95 views

DSolve not giving solution expected

I'm trying to solve the ODE $\frac{\partial M}{\partial \tau} = [ 4 c_3 N(\tau) + c_1 ] M(\tau),$ where $N(\tau) = \frac{q}{2 c_3} \frac{ 1 }{c_2 e^{2 q \tau} + 1} - \left ( \frac{ q + c_1}{4 c_3} ...
0
votes
0answers
381 views

Solving a linear fourth-order fractional integro-differential equation

Definition: A real function $f(x)$, $x>0$ is said to be in space $C_\mu$, $\mu\in \Bbb R$ if there exists areal number $p$ ($>\mu$), such that $f(x)=x^pf_1(x)$, where $f_1(x)\in C[0,\infty]$, ...
0
votes
0answers
118 views

Plotting a function by converting it to a delayed differential equation

I am having a little trouble calculating the Dickman Function from scratch. I have downloaded the notebook from the above link and the have following code: ...
5
votes
1answer
165 views

Working with a system of differential equations that cannot be solved explicitly

I have to work a lot with three functions $\;o_1(t), o_2(t), o_3(t)\;$ that are solutions to the certain system of differential equations: ...
7
votes
2answers
377 views

Nonrectangular region for NDSolve

I have a PDE with mixed boundaries (Neumann and Dirichlet on some sides) in the region $(t,x,y) \in \left( 0, T\right) \times\left\{ -L \leq x \leq L, 0 \leq y \leq h(x) \right\}$ where $h(x)$ is ...
10
votes
1answer
205 views

Inconsistent behavior of WhenEvent[ ]

Consider the following simple example: ...
1
vote
2answers
112 views

Problems with WhenEvent

Any help/explanations will be highly appreciated: This works: ...
0
votes
0answers
22 views

How can I obtain absolute result for Root[ # ] symbol [duplicate]

I'm using mathematica 8.0. When I calculate NDSolve`ImplicitRungeKuttaGaussCoefficients[10, Infinity] function, it gives me some symbolic results. I trided //N and //FuıllSimplify operation as in How ...
5
votes
2answers
476 views

Finding a 3d curve from torsion and curvature with NDSolve

I'm trying to use the Frenet–Serret formulas to find the curve that matches the torsion and curvature I specify numerically with an InterpolatingFunction. The ...
1
vote
0answers
127 views

No response from DSolve

Using optimal control theory, I am trying to find the optimal paths of d and k such that they will maximize profit as given by lc: ...
3
votes
0answers
66 views

Understanding NDSolve::ndsz

I'm working on a largeish system of differential equations where I encounter the NDSolve::ndsz step size is effectively zero; singularity or stiff system suspected ...
2
votes
1answer
235 views

Resonance Curve using NDSolve

I am trying to make a resonance curve like this one below, using NDSolve. I tried to use code as below. Basically I try to hold solution for a w (driving frequency value) using NumericQ and then ...
1
vote
1answer
743 views

shooting method and stifness problem for NDSolve

I'm trying to solve numerically the following differential equation: 1/r[x]^5 + k/Sqrt[1 + r'[x]^2] - (k r[x]r''[x])/(1 + r'[x]^2)^(3/2) == 0 I can set boundary ...
1
vote
0answers
417 views

DSolve 2nd Order Coupled Partial Differential Equations

I am trying to use Mathematica to solve 2 coupled differential equations. My equations are of the form \begin{equation}\ddot{x}_i + A_{il} \partial^l A^{jk} ( \dot{x}_b \dot{x}_c - y_b y_c ) =0 ...
0
votes
0answers
201 views

Crank-Nicolson scheme for Schrodinger equation

I try to solve 1D Schrodinger equation with Crank-Nickolson methode. I use atomic units: time < 10^-14 => 413 a.u.t. length 30 * 10^-9 m => 567 Bohr radii ...
5
votes
1answer
379 views

Detecting a collision in n-body simulation with NDSolve

Consider this three-body system: ...
9
votes
1answer
467 views

How to solve a stiff nonlinear second-order ode?

I want to solve a nonlinear second order ODE as an initial value problem (IVP). Unfortunately, for certain values of first derivative at starting point I get a stiff-problem. I tried to overtake this ...
2
votes
1answer
393 views

How can I solve my system of differential equations?

I have a question pertaining to my code below: I require to find the values of the roots E2 that will set the function ...
5
votes
2answers
279 views

Manipulation of InterpolatingFunction

Suppose that $q[t]$ is obtained by NDSolve as an InterpolatingFunction, and I want to define $Q[t]$ to be some function of ...
-2
votes
1answer
130 views

Can anyone help to solve this set of coupled ODE? [closed]

After some time Mathematica just give me the same thing while I was trying to solve: DSolve[{3 E^(-[Lambda]2 [Phi]0) r a[r] - 1/2 [Lambda]1 [Phi][r] + 3/8 E^(-[Lambda]2 [Phi]0) [Lambda]1 ...
1
vote
1answer
225 views

Plotting equations of motion of a baseball

So I went through the physics of a baseball and I got the exact same equations as shown here on page 8. I input all of the same parameters into my code, and I don't get the same thing. Any idea ...
0
votes
0answers
111 views

Reading Eigenvalue / Eigenfunction result from Reduce

I am trying to find the eigenvalue/eigenfunction solution to: $$\tag 1 y''+3y + \lambda y=0 ; y'(0)=0, y'(\pi)=0$$ I used DSolve and Reduce and they seem to converge, however (embarrassingly) I am ...
4
votes
1answer
170 views

Ordinary differential equation invloving the function composition

I want to solve the following function: DSolve[(A1*Exp[B1*f[x]] + A2*Exp[B2*f[x]])*f'[x] == A1*Exp[B1*x] + A2*Exp[B2*x], f[x], x] And this is what I get as an ...
4
votes
1answer
113 views

NDSolve`ImplicitRungeKuttaGaussCoefficients doesn't work

I am using Mathematica 9.0 on Ubuntu. I tried the first example from this documentation page, but it returns unevaluated: ...
2
votes
1answer
83 views

Will I be able to use NDSolve, and then how

So I am completely new to Mathematica, so sorry if this is a dumb question. I have a set of 3 coupled nonlinear differential equations. They are (a,b,c,D,L constants): ...
0
votes
3answers
311 views

Solving a differential equation with mixed conditions using DSolve

I want to solve a differential equation $$ \frac{d}{dx}\left(k_0 \left(\frac{T(x)}{T_0}\right)^n \frac{dT(x)}{dx}\right)=0,$$ with boundary conditions: $T(l)=T_0$, $\;T'(0)=-\frac{q_0}{k_0 ...
0
votes
0answers
59 views

How to solve initial value problem using Runge-Kutta method? [duplicate]

How to solve the following initial value problem using Runge-Kutta method u''[x] + (2/x) u'[x] + E^(u[x]) == 0, u[0] == 0, u'[0] == 0
0
votes
1answer
103 views

Solving NLODE with substitution

I am trying to get a solution to a non-linear ODE, below is the code that works for my problem. ...
0
votes
1answer
101 views

Transformation of the NDSolve result into new dependent variables

I have solved a set of coupled differential equations and now I need to convert them into different dependent variables and sketch their trajectories. Here is the code I have written so far: ...
0
votes
0answers
369 views

Dsolve not working

I am new to using DSolve. In trying to solve a differential equation I was getting nonsense from Mathematica, so I tried to solve an even easier equation ...
4
votes
5answers
418 views

Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
1
vote
0answers
263 views

Differential equations: How do I solve a delay differential equation with 0-1 variables

How do I solve the following non-linear, delay-differential equations using Mathematica under the assumptions $$p(t) = 1 ,\; y(t) > k$$ $$p(t) = 0,\; y(t)<= \ k$$. $$ \frac{dw}{dt} = ...