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

learn more… | top users | synonyms (3)

0
votes
0answers
67 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
149 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
106 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: ...
4
votes
5answers
567 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
428 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} = ...
11
votes
2answers
759 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 ...
1
vote
0answers
511 views

Why DSolve and NDSolve give different answer

Consider these code, which solve the same equation using DSolve and NDSolve, why do they give different answer? Which one is ...
9
votes
1answer
951 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: ...
4
votes
1answer
158 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
198 views

Plotting basin boundary

How to plot the basin boundary in Mathematica? I have been trying to do this using the system ...
2
votes
2answers
222 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
346 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
790 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
122 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
2answers
648 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
221 views

Why the result by hand is different from the built-in DSolve?

Yesterday, I used the Mathematica to solve a differential equation by the built-in command DSolve: ...
5
votes
1answer
266 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
415 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
452 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
941 views

Solving a system of non-linear differential equations

I want to solve the system of non-linear differential equations given below numerically. $$y''(t)+500y'(t)+100y(t)=-33\cos(500t)-66\cos(1000t)$$ $$300x'(t)=1000y(t)+500y'(t)-35\tanh(50x'(t))$$ ...
11
votes
1answer
434 views

Inconsistent results of second derivative of inverse fourier transform

Bug introduced in 9.0 or earlier and persisting through 10.2.0 I am trying to get the Green's function of a toy diffusion equation $$\frac{\partial^2 u(x,t)}{\partial x^2} = ...
3
votes
1answer
220 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
134 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
105 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
89 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
513 views
1
vote
0answers
288 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
188 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
142 views

DSolve bvfail “For some branches of the general solution, unable to solve the conditions”

I have a problem with the DSolve function and its usage: ...
2
votes
1answer
183 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
130 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 ...
8
votes
1answer
442 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
137 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
1k views

DSolve to solve a system of differential equations [duplicate]

I need to solve a system of differential equations as follows: ...
10
votes
2answers
393 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
218 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
461 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
95 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
945 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
151 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
197 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
693 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 ...
1
vote
1answer
2k views

Singularity / stiffness / precision errors with NDSolve

I have a relatively simple 2nd Order ODE problem I'm trying to solve numerically $p'' + \frac{1}{r}p' = A(\frac{p(r)}{p(r) + k_{m}})$ where $A = 7.5795*10^9$ and $k_{m} = 1$. So trying to get ...
4
votes
1answer
753 views

Numerical solution of Bessel-like equation using NDSolve

I need to calculate solution of Bessel-like equation having general form: $\frac{d^2F}{dr^2}+\frac{1}{r}\frac{dF}{dr}+Q(r)F(r)=0$. Problems come from the points near $r=0$ leading to numeric errors. ...
0
votes
1answer
211 views

PDE Solving in mathematica

I'd like to ask how I might go about solving this equation: $\frac{\partial Ci}{\partial t} + \frac{1}{r^2}\frac{\partial (r^2 Ci)}{\partial r} = D\frac{1}{r^2}\frac{\partial}{\partial ...
1
vote
1answer
231 views

Defining a curved region for NDSolve

I have an equation to solve using NDSolve which involves two parameters: $en$ and $k$. The equation produces a set of curves when $en$ is plotted against $k$. In ...
1
vote
0answers
148 views

parameter NDSolve

the question I need to solve is: t x'[t] == -x[t] + y[t], t y'[t] == -5 t^2/x[t]^2 + x[t] - y[t], x[1] == 4, x[b] == 1 in order to solve the coupled ...
0
votes
1answer
988 views

How to change machineprecision digits

I am trying to compute t0: ...
2
votes
1answer
552 views

How to work with differentials explicitly?

When working with differential equations with independent (e.g. t )and dependent (e.g., x[t]) variables Mathematica expresses ...
3
votes
1answer
2k views

Can Mathematica solve integro-differential equations?

I have integro-differential equations like this: ...