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

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12
votes
1answer
202 views

“ParametricSensitivity” in ParametricNDSolve

"ParametricSensitivity" is listed as a Method in the documentation for ParametricNDSolve, ...
1
vote
0answers
62 views

Solving an ODE using shooting method [duplicate]

I have been trying to solve the following nonlinear ordinary differential equation: $$-\Phi''-\frac{3}{r}\Phi'+\Phi-\frac{3}{2}\Phi^{2}+\frac{\alpha}{2}\Phi^{3}=0$$ with boundary conditions $$\Phi'(...
2
votes
0answers
61 views

Solving a differential equation with a complex (independent) varible

I'm trying to plug in complex values in the numerical solutions of ODEs without success. For instance y[I] /. NDSolve[{y'[x] == 0, y[0] == 3}, y, {x, -10, 10}] ...
-1
votes
1answer
128 views

Problem with NDSolve and If

If T=T1, program can calculate. But, when T = T1*If[Abs[q2[t] - q2d] < e1 && Abs[q2'[t]] < e1, 0, 1], program can ...
0
votes
1answer
105 views

DSolve Error 3D Navier Stokes (z,r,t)

I am essentially wanting to solve Navier Stokes in the [z,r,t] dimensions (2D+Unsteady Flow) for pressure driven flow. However, I keep getting an error I am unable to resolve in my Dsolve such as: ...
2
votes
1answer
125 views

ODE of an eccentric circle

How can we simplify the solution in: DSolve[ {Sqrt[ 1 - (r[t] - T^2/r[t])^2/(2 a)^2]/(r[t] - T^2/r[t])/(2 a) == r'[t]/ r[t], r[0] == T}, r, t] (r,t) are polar ...
1
vote
2answers
74 views

Condition on Inside of Region

How do I handle boundary conditions present in the region. Mathematica complains about the condition v [1 , t ] == u [1,t]. The condition should be given to this ...
4
votes
3answers
635 views

Nonlinear differential equation: numerical solution

I have to find and plot a numerical solution for this second order differential equation: u''[x] + (u'[x]/x) - (u[x]/(x^2)) + u[x] - u[x]^3 = 0 where $0\leq x &...
1
vote
1answer
81 views

How do I restrict the range of an interpolating function in NDSolve?

I have a numerical solution for a differential equation. I know that the gray dotted solution is unphysical. Is there a way I can tell mathematica to ignore the gray dotted solution (e.g. restrict the ...
0
votes
1answer
133 views

How to solve time dependent coupled differential equations? [closed]

I am trying to solve time dependent coupled differential equations with know initial conditions. I am just a beginner in terms of coding so would really appreciate if someone can give me an example of ...
1
vote
1answer
122 views

Getting the message NDSolve::underdet:

I am solving the wave equation with initial position and velocity function: ...
0
votes
1answer
70 views

NDSolve does not satisfy initial conditions

For the problem I'm facing, I have three coupled diff eqns that I'm trying to solve ...
0
votes
2answers
253 views

How to solve a pair of coupled 2nd order equations using shooting method

I have a pair of equations for x[t] and y[t]. Both are 2nd order and they are coupled. Now say that I know the following ...
0
votes
0answers
41 views

Boundary condition [duplicate]

I'm having the following issue that can not find a solution , by using this boundary condition v[0, t] == u[1, t] that Mathematica does not understand, someone ...
0
votes
1answer
193 views

Improving NDSolve computation speed for 3D stationary PDE

Continuing my last question, I am trying to solve 3D Schrodinger equation (with mass equals to 1) and with no potential (I will add a potential later). The analytical solution for this equation is ...
2
votes
1answer
147 views

Equal flow boundary conditions

I'm having the following issue that can not find a solution , by using this boundary condition v[0, t] == u[1, t] that Mathematica does not understand, someone ...
7
votes
2answers
239 views

Extending NDSolve beyond a singularity

The $\tan$ function satisfies the following IVP: $$y'=1+y^2 ,\quad y(0)=0 $$ and has simple poles at the points $x=\pi/2+ \pi n$ for integer $n$. When trying to get $\tan$ via numerical integration,...
0
votes
2answers
142 views

Convert DE to first order?

I have the following set of second-order differential equations: ...
5
votes
4answers
240 views

How should I deal with messages being produced by my Manipulate?

I have made a knockoff of John Polking's dfield for a web-embedded CDF (via Enterprise Mathematica). My code extends that from Belisarius who last year showed me how to use ...
0
votes
1answer
86 views

Problems with solving two coupled lorenz equation with NDsolve

I have a system of two coupled lorenz equations and I'm to integrate it: ...
1
vote
0answers
50 views

NDSolve error with a given system of equation [closed]

I know that my question will be very similar to NDSolve giving NDSolve::deqn: message when given my system of equations . Sorry for that, I am so new on Mathematica. I have tried to use the ...
0
votes
1answer
149 views

How to speed up NonlinearModelFit applied on a NDSolve solution?

I'm trying to perform fittings of a model defined through a system of ODEs to data consisting of time courses of a measured quantity. As described in a previous question, the system of ODEs is as ...
2
votes
0answers
279 views

NDSolve fixed step problem

Working example here: Drive folder (have both files in the same directory! Notice: the line <<variables' in the file seems to throw an error for me, but ...
3
votes
1answer
92 views

DSolve: Why does Mathematica does a separate integration from 0 instead of 1 and then from 1 to upper limit?

I am trying DSolve in Mathematica for an ODE. Here is the command I am trying and the result I get DSolve[{x'[t] + y[t] x[t] == 0, x[0] == x0}, x[t], t] $$ \left\...
5
votes
1answer
137 views

List of unknowns in a differential equation

I often find myself wanting to see what variables/constants are undefined in a large set of differential equations, is there a function that will do this for me? As an example, for the following ODE ...
2
votes
1answer
107 views

Fails to apply NonlinearModelFit on a numerically evaluated model defined as a system of ODEs

I call for your help with because I'm getting troubles to fit a model defined through a system of ODEs. The system of ODEs is as follows: ...
2
votes
1answer
166 views

solving coupled differential equations with parameters subject to optimization problem

I have an equation, but I don’t know how to program it in Mathematica: x[0]==1; y[0]==1; x'[t]==(a+b) x[t] y[t]; y'[t]==a b y[t]/x[t]; where ...
4
votes
2answers
282 views

NMinimize Constraints on Interpolating Functions

I have the following piece of code and am trying to use NMinimize (the last line in the following chunk of code) to minimize ...
1
vote
1answer
41 views

Reverse order in evaluated list

I solve the following set of ODE and plot solution of S1 vs k2 (Figure 1). ...
7
votes
1answer
205 views

Why should the spatial derivative order of the ODE *not* exceed two?

Following this question I came across this strange behaviour. Let me define a 1 D interval implicitely ...
7
votes
3answers
392 views

FEM Solution desired for “Plate with orifice” deflection: Application of Boundary Conditions and use of Regions

I found the deflection of an orifice plate (circular plate with a hole) subject to uniform pressure using Mathematica's NDSolve functionality. The plate is fixed at its outer circumference and is ...
11
votes
2answers
187 views

Integration of a PDE solution over a custom-defined subdomain

Preamble: In my previous question I raised a problem of a custom-chosen integration of the solution of a PDE. In that case it was an integration along a line lying within the PDE domain. The solution ...
3
votes
1answer
142 views

Increasing NDSolve computation range for 3D stationary PDE

I am trying to solve 3D Schrodinger equation (with mass equals to 1) and with no potential (I will add a potential later). My goal is to set boundary conditions on the outer boundary of a sphere and ...
2
votes
1answer
201 views

Solving SDE: $\frac{dy(t)}{dt}=(c+\sigma_wW(t))y(t)+\epsilon(t) $ in Mathematica

I want to solve this differential equation $\frac{dy(t)}{dt}=(c+\sigma_w W(t))y(t)+\epsilon(t) $. For details see http://math.stackexchange.com/questions/1385633/solving-sde-fracdytdt-c-sigma-wwtyt-...
8
votes
1answer
206 views

SymplecticPartitionedRungeKutta shows strange error

Bug introduced in 9.0 or earlier and persisting through 10.2 or later I tried to solve Hamiltonian system ($Q$ is a vector of all generalized coordinates, $P$ - of generalized momentum) $$ \frac{\...
2
votes
0answers
46 views

NDSolve with NIntegrate [duplicate]

I'm new to Mathematica and I'm trying to use it to solve some equation like: NDSolve[x'[t]+NIntegrate[x[tau],{tau,0,t}]==20,x,{t,0,10}] But it keeps giving me ...
1
vote
1answer
73 views

Matrix issue with NDSolve

I am solving a differential matrix equation with NDSolve. ...
2
votes
1answer
122 views

Problem in understanding PDE solution

I solved the PDE shown below and I got the solution. I am new to this tool. In the solution, I have a constant multiplied by a vector like function (please refer second term of the solution). What ...
1
vote
1answer
72 views

Trouble solving a system of partial differential equations [closed]

I am trying to solve a system of linear PDEs analytically and I dont get the answer. I am new to this tool, appreciate your help ...
0
votes
1answer
94 views
1
vote
0answers
54 views

Transform a vector DE into a set of scalar DEs [closed]

I have the vector equality: {{a,b},{c,d}}.D[{x1[t],x2[t]},t]=={{e,f},{g,h}}.{u1[t],u2[t]} I want to solve this using DSolve. ...
7
votes
1answer
459 views

Dipolar magnetic field lines inside a cylinder

I'm drawing the magnetic field lines of a rotating dipole (magnetic field distorded by emission of radiation). Currently, my Mathematica 7.0 code is fully working, but I'm having a constraint which I ...
5
votes
1answer
95 views

In a PDE solution let us integrate out one of two coordinates

Here is a trapezoid within which I am solving a simple Laplace equation with the Dirichlet boundary conditions set at its top and bottom: ...
0
votes
1answer
131 views

The length of the derivative operator Derivative[0,0,2,0] in \ f^(0,0,2,0)[x,y,z,t] is not the same as the number of arguments. >>

I'm trying to solve Maxwell's wave equation but am faced with an error message ...
0
votes
1answer
63 views

Problem with solving coupled differential equations

The following code seem to produce an output that appears to be independent of the parameter "fg". It is possible that the way the code is written might be causing it, but how can one fix this problem....
0
votes
0answers
43 views

Is there a way to pre-calculate a slow animation and then run easily with no lag? [duplicate]

I have an animation of a triple pendulum on a moving base, however even after trying to change the whole coding to make it faster by using module and all it is still pretty bad as I need it to be ...
6
votes
1answer
125 views

code is ignoring WhenEvent

I would like the value of x[t] to be equal to 0 when it has a negative value so I used WhenEvent but it has no effect on my code ...
-2
votes
2answers
94 views

Error in the solving of the simultaneous Ordinary Differential Equation [closed]

As I am trying to get the solution of the simultaneous ordinary differential equations ...
7
votes
0answers
229 views

DSolve returns an answer that is not a solution

Investigating DSolve misses a solution of a differential equation, I came across this odd behavior of DSolve. The following DSolve command returns an answer to the ...