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

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0
votes
1answer
193 views

Using NDSolve for three variables as function of time

I want to be able to plot z, and r. Should I be using DSolve, NDSolve or something else? I've tried to clear it up a bit Thanks, Will ...
3
votes
1answer
286 views

Solving Rotational Equations of Motion

I'm trying to integrate the rotational equations of motion ...
0
votes
1answer
102 views

Check when DSolve returns input [closed]

I'm making a program where i need to plot the soluton of an ODE and ,if possible, obtain the analytical solution. My idea was to use DSolve, check the output, and if it failed use NDsolve. Now, i ...
10
votes
1answer
1k views

How to solve a system of partial differential equations?

Edit: since the upgrade to Mathematica 10, this problem seems solved I just want to solve a system of partial differential equations, for example: $$ \left\{ \begin{array}{l} ...
1
vote
1answer
152 views

Boundary condition is not specified on a single edge of the boundary of the domain

I am attempting to solve a PDE as prescribed in a paper I am reading; however, Mathematica doesn't seem to be happy with the way I am posing the problem. Im my case, r(t,100) is an approximation of ...
0
votes
0answers
43 views

Write nth line to file [duplicate]

I have a code that I am running on a supercomputer. Currently the algorithm must finish before I can export any results from the algorithm. What I would like to do is to have the algorithm write out ...
-1
votes
1answer
114 views

how to solve this ode problem? [closed]

NDSolve::ndnum: Encountered non-numerical value for a derivative at x \ == 0.`. >>
0
votes
1answer
98 views

Cannot get specific value from NDSolve (multiple functions)

I am trying to solve six connected differential equations. This is my code: ...
1
vote
1answer
262 views

Need help with solving a second order differential equation

I need help with solving this differential equation. ...
-1
votes
1answer
109 views

Solve set of non linear differential equations [closed]

I have set of differential equations. For example, I took two equations and tried to solve them as below. I am not getting any results. Please help me to figure it out the mistake. And I wonder if I ...
3
votes
1answer
239 views

Solving a constrained vector system with NDSolve

I'm trying to replicate the pendulum DAE example in the Documentation Center (example/ModelConstrainedSystemsAsDAEs) using Mathematica 9's vector support with NDSolve. So far I have: ...
0
votes
0answers
71 views

Nonlinear System of ODEs

I want to solve this NonLinear System: $$\Theta_{\xi} = \frac{(1-\lambda)K_{\alpha}}{\beta}\Phi^{2}\Theta+\frac{2\beta-1}{6\beta}\xi\Theta$$ $$\Phi_{\xi} = \frac{1}{2\lambda K_{\alpha}\ ...
1
vote
1answer
315 views

Use Euler method to solve differential equation

Use Euler's Method or the Modified Euler's to solve the differential equation ${dy/dt=y^2+t^2-1, y(-2)=-2}$ on $[- 2, 2]$. Take h = 0.2 (...
2
votes
1answer
129 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
133 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
97 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
297 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
163 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
69 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
165 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
181 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
53 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
236 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
211 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
97 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
242 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
128 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
109 views

Eliminate complex answer to differential equation

I've tried the following: ...
0
votes
2answers
148 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
150 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 ...
7
votes
0answers
132 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
42 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
386 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
165 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
137 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 ...
9
votes
3answers
864 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
109 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
258 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
201 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
375 views

Error messages from NDSOlve

I am trying to solve a boundary value problem with NDSolve. The code is: ...
0
votes
0answers
89 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
357 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
109 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
159 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
314 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
203 views

Inconsistent behavior of WhenEvent[ ]

Consider the following simple example: ...
1
vote
2answers
106 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 ...
5
votes
2answers
443 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
108 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: ...