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

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0
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1answer
145 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
130 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 ...
4
votes
1answer
135 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
173 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
402 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
320 views

Solving a system of non-linear differential equations

I want to solve the system of non-linear differential equations given below numerically. $$y''(t)+500y'(t)+100y(t)=-33\cos(500t)-66\cos(1000t)$$ $$300x'(t)=1000y(t)+500y'(t)-35\tanh(50x'(t))$$ ...
8
votes
1answer
252 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
113 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
102 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
88 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
84 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
180 views
1
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0answers
176 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 ...
4
votes
1answer
94 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
91 views
1
vote
1answer
145 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
86 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
397 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
108 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
278 views

DSolve to solve a system of differential equations [duplicate]

I need to solve a system of differential equations as follows: ...
8
votes
2answers
258 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
198 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
238 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 ...
1
vote
1answer
72 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. ...
10
votes
1answer
500 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
111 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
122 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
395 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
377 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 ...
3
votes
1answer
321 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
0answers
73 views

DSolve is rejecting my description of a system of PDEs

I am trying to solve a system of partial differential equations using DSlove. But i get the input equations in return. Dsolve is not doing anything ...
0
votes
1answer
138 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 ...
0
votes
0answers
89 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
122 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
180 views

How to change machineprecision digits

I am trying to compute t0: ...
0
votes
0answers
79 views

Parameter sensitivities of ParametricNDSolveValue involving numerical function

This is a followup of my former question from here. Consider the code ...
2
votes
1answer
191 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 ...
1
vote
1answer
776 views

Can Mathematica solve integro-differential equations?

I have integro-differential equations like this: ...
1
vote
1answer
159 views

Using ParametricNDSolveValue with initial conditions of another ParametricNDSolveValue

I have a system of parameter-dependent ODEs, which I can solve using ParametricNDSolveValue. Now, I have another ODE, which has as initial condition the solution of ...
0
votes
0answers
313 views

Solving differential equations with sums (power series)

I have sets of 10 differential equations, but for this purpose I'll demonstrate what I need on one example that can be solved by hand. My equation is this: ...
8
votes
3answers
619 views

Can Mathematica solve this sort of functional/differential equation?

I am looking for differentiable functions $f$ from the unit interval to itself that satisfy the following equation $\forall\:p \in \left( 0,1 \right)$: $$1-p-f(f(p))-f(p)f'(f(p))=0$$ Is there a way ...
0
votes
0answers
455 views

PDE problem with initial and boundary conditions

I'm new to mathematica and I don't know what I do wrong, I have written the following PDE problem, with both initial and boundary (four in total) ...
12
votes
1answer
731 views

Numerical solution of coupled ODEs with boundary conditions

I have to solve the following set of ODEs and just can't get good results using Mathematica $$ r\frac{d}{dr}\left(\frac{1}{r}\frac{d}{dr}A(r)\right)-\xi^2F(r)^2\left(A(r)-1\right)=0 $$ $$ ...
1
vote
1answer
221 views

Solve a total derivative - independent vs. dependent variables

I am trying to force mathematica to solve a generally defined function for d lp: In a reduced version, w depends on l2, ...
0
votes
2answers
940 views

Solving a system of nonlinear coupled ODEs

I tried using NDSolve to solve the following system of equations: ...
1
vote
0answers
128 views

NDSolve error when solving pde

I am trying to calculate speed of viscous fluid in a rotating hollow sphere. The sphere is rotating round z axis. The fluid is incompressible. I used Navier-Stockes equations. The only boundry ...
1
vote
0answers
167 views

Jumps in NDSolve results

I need to compute using NDSolve routine, some function $F(x)$, having two possible values $F_1(x)$ and $F_2(x)$ depending on whether the argument exceeds some ...
0
votes
0answers
81 views

Nested NDSolves with functions

I am trying to solve a system of nested differential equations, and have attached my code below. The first section is some variable declarations, then I solve my first diffeq and store the solution to ...
0
votes
1answer
66 views

LMS distance from a point to an InterpolatingFunction

I have a short script to NDSolve a second-order nonlinear BVP, which as its output produces an InterpolatingFunction object. I ...
6
votes
1answer
375 views

Getting clearer StreamPlot output

When I do a StreamPlotof a rather complicated pair of differential equations, it loses some details. For example: ...