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

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5
votes
2answers
430 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 ...
1
vote
1answer
256 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
131 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
223 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
131 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
86 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
347 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
65 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
118 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
104 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
546 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
497 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
343 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
517 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 ...
9
votes
1answer
683 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
137 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
175 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
189 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
267 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] ...
9
votes
1answer
658 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
votes
0answers
111 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
497 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
180 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 ...
0
votes
0answers
248 views

Linear Stability Analysis Routine. Normal Modes in NDSolve

I want to make the linear stability analyis of a nonlinear system of PDEs. So for example then I want to plot what happens to the amplitudes of the modes. To do that I need to solve my equations with ...
5
votes
1answer
195 views

WhenEvent method with 3 conditions

I am trying to solve system of differential equations below $$x''(t)=-2.25cos(1.5t)-x(t)-x'(t)$$ $$y''(t)=-1.125cos(1.5t)-4y(t)-y'(t)$$ $$z'(t)=\begin{cases}x(t)-(1+y(t)), & \text{if } ...
3
votes
0answers
304 views

Numerically solving a system of PDEs where one function is composed with the other

I'm trying to solve the following system using NDSolve: $$ \begin{align} u_t(x,t) &= u_{xx}(x,t) - v(x,t) \\ v_t(x,t) &= u(v(x,t),t) \end{align} $$ with ...
5
votes
3answers
433 views

Solving recurrence sequence using an ODE

I'm trying to solve the recurrence a[n] == 0 for n < l a[l] == 1 a[n] == (l + 2(n - l) a[n - l] + (n - l)(n - 1) a[n - 1])/n(n - l + 1) for n >= l using ...
1
vote
1answer
659 views

Solving a system of non-linear differential equations

I want to solve the system of non-linear differential equations given below numerically. $$y''(t)+500y'(t)+100y(t)=-33\cos(500t)-66\cos(1000t)$$ $$300x'(t)=1000y(t)+500y'(t)-35\tanh(50x'(t))$$ ...
10
votes
1answer
395 views

Inconsistent results of second derivative of inverse fourier transform

I am trying to get the Green's function of a toy diffusion equation $$\frac{\partial^2 u(x,t)}{\partial x^2} = \frac{1}{\alpha^2}\frac{\partial u(x,t)}{\partial t}$$ with Mathematica 9. Then solve ...
3
votes
1answer
196 views

Changing equations to be solved by NDSolve when an event is triggered

I am using NDSolve to solve a set of coupled differential equations. When a certain event occurs, I want two equations in the set to be changed radically, for example from ...
0
votes
1answer
127 views

Problem evaluating results of DSolve (Power::infy)

So, after browsing through older posts to see if anybody else could have had the same problem, I have come to the conclusion that I am stuck. That bothers me, especially because it should be straight ...
0
votes
1answer
99 views

How to combine DSolve and FindRoot

As my differential function is relatively complex I do not want to do the detour of finding an explicit solution via DSolve for it but rather use an FindRoot-like approach by guessing initial starting ...
-5
votes
1answer
88 views

Converting function into differential version

I am looking through a journal and I came across a function that I wanted to convert to its differential version using Mathematica. Would anyone be able to get the differential version by using ...
4
votes
1answer
393 views
1
vote
0answers
236 views

What am I doing wrong when using DSolve

I'm trying to solve a simple PDE in Mathematica. I just can't get Mathematica to give me an explicit analytical solution. This is the code that I made and it basically repeats in the output what I ...
6
votes
2answers
154 views

How to use WhenEvent with a vector ODE in NDSolve

I have an ODE system I'd like to specify as a vector equation in NDSolve. I'm not clear on how to use WhenEvent for a system ...
1
vote
1answer
119 views
1
vote
1answer
169 views

Writing NDSolve-like functions

I've been using Mathematica for a while now, and there are multiple common tasks that I end up doing. I'd like to learn how to convert them into functions so that I can store them in some file and ...
2
votes
0answers
112 views

How to solve system of differential equations of arbitrary order (symbolic tensors)?

I am interested in solving systems of ODEs symbolicly, keeping things with arbitrary dimensions for clarity. For example, assume that $x, f(x) \in R^N$ and $A \in R^{N \times N}$, how do I solve ...
7
votes
1answer
432 views

Issue with the NDSolve code

With this procedure, one may determine an eigen-value function $R(a)$ for any given $\Xi$ (say 0, 25, 50, 75, 100) ...
4
votes
2answers
122 views

Non-convergance of the solution of the 1+1 partial differential equation

I am stacked with a partial differential equation as follows: This is the $\LaTeX$ expression for the equation $$ \frac{\partial y}{\partial t}=\frac{\partial^2 y(x,t)}{\partial x^2} ...
0
votes
1answer
952 views

DSolve to solve a system of differential equations [duplicate]

I need to solve a system of differential equations as follows: ...
10
votes
2answers
343 views

How to draw the image of a circle under the action of a transformation of the phase flow?

How to draw the image of a circle $x^2+(y-1)^2<1/4$ under the action of a transformation of the phase flow for the equation $\dot{x}=y,\ \dot{y}=-\sin x$? Here $\dot{x}$ means $dx/dt$. Any help or ...
4
votes
0answers
216 views

Using FindFit to fit nonlinear ODE parameters, subject to a constraint (an inverse problem) [duplicate]

Similar to this post I am finding that constraints tend to make FindFit poor at finding a good fit. However, unlike the previous post, the constraints are required ...
0
votes
3answers
394 views

Differential equation of mass spring system with compliant stoppers

I would like to solve numerically the differential equation for the displacement x[t] of a mass m-spring ...
2
votes
1answer
86 views

Export to CDF fails

The code below generates the error when I attempt to export to CDF Preview: Coordinate {xde[4.69588928222656], yde[4.69588928222656]} should be a pair of numbers, or a Scaled or Offset form. ...
12
votes
1answer
788 views

Solve a PDE on a domain $\Omega$ with given boundary conditions

I'm starting to study the behavior of some PDEs and I would like to run simulations in mathematica to help me visualize solutions. For example, a prime example that I would like to study is $$ ...
0
votes
1answer
136 views

Manipulating and using result of DSolve

I have an unsightly looking equation that nonetheless has an analytical solution. The solution is ugly as hell, but exists; I use the following code with the DSolve ...
1
vote
1answer
167 views

DSolve expression not evaluating

I entered the following into Mathematica: p[x_] := 4 x q[x_] := 4 Sqrt[x] - 3 f[x_] := E^-Sqrt[x] DSolve[y''[x] + p[x] y'[x] + q[x] y[x] == f[x], y[x], x] ...
2
votes
1answer
563 views

Differential equations: Solving a singular/nonlinear ODE using NDSolve

I am trying to numerically solve a rather horrible looking singular/nonlinear ode: A*(y''[x]/y[x])'' +y[x]^2==1 on the interval ...