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

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0
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0answers
102 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
248 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
193 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
335 views

Error messages from NDSOlve

I am trying to solve a boundary value problem with NDSolve. The code is: ...
0
votes
0answers
87 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
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0answers
339 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
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0answers
107 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: ...
2
votes
1answer
141 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
291 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 ...
9
votes
1answer
200 views

Inconsistent behavior of WhenEvent[ ]

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

Problems with WhenEvent

Any help/explanations will be highly appreciated: This works: ...
0
votes
0answers
21 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 ...
4
votes
2answers
403 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
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0answers
103 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
60 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
205 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
583 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 ...
0
votes
0answers
144 views

Second-order DSolve overdetermined with only 2 boundary conditions

I was going through some circuit analysis problem and came up with a second-order differential equation, which I decided to solve with Mathematica: $$ L\frac{\mathrm{d}^{2} I}{\mathrm{d}t^{2}} + ...
0
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0answers
140 views

“Hard” ODE with three kind of solution: IVP or BVP?

I want to solve numerically the second-order differential equation proposed by Coleman in this paper (equation 8, page 1804): $$ \gamma(\lambda) \lambda_{zz} + \beta(\lambda) \lambda_z^2 + ...
1
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0answers
322 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
190 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 ...
0
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0answers
116 views

Solving simple ODE for eigenvalues causes nightmares

I had some code which could solve an ODE for the function $u$ and the eigenvalue $E$. Unfortunately, $E$ is a function of another parameter $k$. This meant, that upon solving the equations, I had to ...
0
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0answers
83 views

Issue with NDSolve

This could be a stupid issue, but I have been checking for ages. I cannot solve this apparently innocuous system of PDEs: ...
5
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1answer
319 views

Detecting a collision in n-body simulation with NDSolve

Consider this three-body system: ...
9
votes
1answer
398 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
379 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
236 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
126 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
200 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
97 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
147 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
106 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
82 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
286 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
58 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
101 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
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1answer
100 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
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0answers
247 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
385 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
235 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} = ...
8
votes
2answers
356 views

How to make use of an interpolating function outside of Mathematica? [duplicate]

I'm currently working on a project where I have to solve some partial differential equations. Initially, I made some approximations so that an analytic solution could be obtained, and my ...
7
votes
0answers
377 views

NDSolve::ndcf: Repeated convergence test failure. How to solve?

I am trying to simulate a system of $n$ pendulums with some friction in Mathematica 9. This is the code I am using: ...
3
votes
1answer
108 views

Nested NDSolve with WhenEvent: setting up new equations and discarding old ones

I am checking a complex situation where a function x1[t1] only exit in a finite time span, and after this a new function x2[t2] ...
1
vote
0answers
139 views

Plotting basin boundary

How to plot the basin boundary in Mathematica? I have been trying to do this using the system ...
1
vote
2answers
150 views

Plot the velocity

So I am trying to find the connection between Forcing Amplitude and Velocity in a differential equation (Which is the part of system of differential equations). Those system differential equations ...
0
votes
1answer
160 views

Bifurcation with a system of equations

I'm trying to plot a flip bifurcation diagram for a dynamical system of equations as follows: x'[t] == v[t] v'[t] == x[t] - A x[t]^3 + R*Cos[\[Omega]*t] - B v[t] ...
8
votes
1answer
406 views

how to simplify large expression with lots of special functions in it (BesselY, Hypergeometric, MeijerG etc…)

I saw this DE in Maple forum. When solving it using Mathematica 9.01, even though the result was correct (both solutions gave the same numerical answer for some random values), Mathematica's answer ...
0
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0answers
101 views

Smoothing a function

NDsolve gives me a solution to a certain NL PDE. I want to evaluate the rate of exponential decay of the maxima of the solutions in time. So, I plot ...
-2
votes
3answers
207 views

Plotting DSolve results

I am attempting to make a plot of the solution an ODE. I want to plot the solution using PolarPlot, x is the polar angle in ...
0
votes
1answer
147 views

Why the result by hand is different from the command “DSolve”?

Yesterday,I use the Mathematica to solve a Differential Equation by the command DSolve: DSolve[y''[x] + 2 y'[x] + 5 y[x] == x Cos[x], y[x], x] {{y[x] -> E^-x ...