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

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2
votes
1answer
117 views

Mathematica can't find constants for this differential equation

I am having problems solving this differential equation: diffeq = m x''[t] == -a E^(b*x'[t]); sol = DSolve[{diffeq, x[0] == 0, x'[0] == v0}, x[t], t] The output ...
0
votes
1answer
111 views

Partial differential equation with initial conditions

And so I want to solve the following equation, subject to these initial conditions: $\ u_{tt} - u_{xx} = 6u^5+(8+4a)u^3-(2+4a)u$ $\ u(0,x)=\tanh(x), u_t(0,x)=0$ When I use NDSolve to solve within ...
0
votes
0answers
88 views

How to solve a ParametricNDSolve issue when the system seems to be stiff?

I have a problem with ParametricNDSolve[]. Mathematica gives the warning that a stiff system is suspected. I have varied the methods but unfortunately I was not ...
5
votes
3answers
291 views

Kinetic Friction in Mathematica, weird behaviour

I found the behavoiur of Sign function weird in the code below. when $T=10$ ...
0
votes
1answer
124 views

Issue with NDSOlve while solving vector differential equation [closed]

I am trying to get solution of a vector differential equation x'[t]= aa*x[s] where aa is my 9X9 matrix ...
0
votes
0answers
54 views

Numerically solving a PDE with dependance on a fixed grid point

I am trying to solve partial differential equations of the type $y^{(1,0)}(t,x) = f(y^{(0,1)}(t,x), y(t,x_0))$ where $x_0$ is a fixed point. For example, when pluging this into Mathematica : ...
1
vote
1answer
124 views

Looping with NDSolve?

I have a series of PDE equations that are solved with NDSolve for certain variables $a$ and $b$ - Now, I want to see the output at a time $t$ as $a$ and $b$ change; so I was thinking of a loop ...
1
vote
0answers
175 views

Complicated condition for system of differential equation

I am trying to solve a series of nonlinear differential equation with complex condition as described by block diagram below. The left figure describes general concepts and the right figure describes ...
1
vote
1answer
52 views

Testing if a specific expression is a solution for ordinary differential equation [closed]

I would like to know what is the full command details of wanting to test if a specific expression is a solution for ordinary differential equation (without using DSolve). Thanking you in advance for ...
1
vote
1answer
182 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
193 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
89 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
235 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
122 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
102 views

Eliminate complex answer to differential equation

I've tried the following: ...
0
votes
2answers
129 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
142 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 ...
6
votes
0answers
122 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
38 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
229 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
142 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
123 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 ...
8
votes
3answers
705 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
97 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
219 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
185 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
293 views

Error messages from NDSOlve

I am trying to solve a boundary value problem with NDSolve. The code is: ...
0
votes
0answers
81 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
280 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
104 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
136 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
251 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
197 views

Inconsistent behavior of WhenEvent[ ]

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

Problems with WhenEvent

Any help/explanations will be highly appreciated: This works: ...
0
votes
0answers
20 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
361 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
88 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: ...
2
votes
0answers
54 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
197 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
528 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
133 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
votes
0answers
136 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
vote
0answers
274 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
187 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
votes
0answers
112 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
votes
0answers
82 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
votes
1answer
300 views

Detecting a collision in n-body simulation with NDSolve

Consider this three-body system: ...
9
votes
1answer
366 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
362 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
219 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 ...