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

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7
votes
1answer
194 views

ODE w/seasonal forcing term

I am working my way through a mathematical modeling book, and I'm having trouble replicating one of the results. The Differential equation is given as: $\frac{dC}{dt} = \frac{F}{V}(C_{in}-C)$, where ...
0
votes
1answer
109 views

How to specify a NeumannValue in a system of non-linear partial differential equations?

I am trying to solve a nonlinear system of partial differential equations. If I assume DirichletConditions it all works well. ...
1
vote
1answer
190 views

Differential equation solution

DSolve[y''[x] + (a - (b*x^2 - c)*x^2)*y[x] == 0, y[x], x] I couldn't solve this equation, please help
1
vote
2answers
123 views

How to rescale the independent variable? [closed]

I use NDSolve to solve several differential equations (same equation, but different defined constants) and then to plot the results. The dependent variable in my ...
2
votes
3answers
227 views

“Unstable” solution of a system of two coupled first order ordinary differential equation

Sorry for the long post. Maybe some of you will read the first few lines and already figure out what's going on, but in case it's not the case, I wanted to give as many details as possible. I came ...
2
votes
2answers
93 views

numerical integration of equation obtained by ParametricNDSolve

I am trying to find a definite integral of the solution obtained using ParametricNDSolve (i.e. y[x,a,b]) from 0 to 1 and plot ...
2
votes
2answers
186 views

Plot of the Mod of NDSolve solutions sometimes connects discontinuous jumps

UPDATE: The answers given are informative, and provide a workaround which has been given in other posts, but is unfortunately not very efficient. There still seems to be a lack of deeper understanding ...
6
votes
2answers
371 views

Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)

On this Mathematica.SE form, there exists information on how to use Mathematica to demonstrate the vibration of a circular membrane and the deflection of an orifice plate (the latter I had raised ...
1
vote
0answers
390 views

Time evolution of a bispinor [duplicate]

The effective Hamiltonian for polariton graphene is given by: ...
5
votes
1answer
142 views

How to plot multi-colored regions separated by InterpolatingFunction on sphere

I would like to plot a sphere with multi-colored regions separated by solutions of a differential equation (no explicit expression is available for the separating curves). The result I am after would ...
0
votes
0answers
46 views

NDSolve emits CoefficientArrays::poly error [duplicate]

I'm trying to numerically solve a reaction diffusion equation in Mathematica, but I'm having trouble with the syntax. When I type in the following code, I get the error below it. I think it might have ...
3
votes
1answer
190 views

Backward in time numerical integration with fixed time step

Consider simple use of NDSolve[] function used to solve an ODE backward in time ...
2
votes
2answers
164 views

Wave equation with piecewise initial condition

I am trying to solve numerically the wave equation with the following initial and boundary conditions: ...
2
votes
0answers
89 views

How to include the radiation from a surface in a heat flow PDE? [closed]

I have a PDE were the temperature distribution T[t,x,y] is to be determined. The region is a cross section of a (glass) plate. On one side I heat using a Neumann condition, on the opposite side I want ...
0
votes
1answer
542 views

What is the meaning of the error message “Set::write: Tag Plus in … is Protected”? [closed]

i'm trying to solve system of 9 coupled linear differential equations.I've this problem ... what is it's meaning?
0
votes
1answer
146 views

Iterating FindRoot to solve a differential equation

I am new to Mathematica style programming, better at traditional programming. I would like to know if I can create a table of results using FindRoot, where the ...
4
votes
1answer
144 views

Help nedeed for understanding NDSolve architecture -Vacuum Heating Simulation

I am a beginner in mathematica and I am facing a problem that is way bigger than my knowledge.. I am tryng to simulate a semplificated version of Brunel Effect, wich is a Laser-Plasma interaction ...
1
vote
0answers
53 views

Getting ALL solutions of the logistic ODE with DSolve?

In Mathematica 10.0, the command DSolve[y'[x] == y[x]*(1 - y[x]), y[x], x] gives {{y[x] -> E^x/(E^x + E^C[1])}} I take ...
3
votes
2answers
139 views

Coupled differential equations from Lagrangian — singularity being reached very quickly

I was wondering if there was a way to help the solutions to these differential equations not hit a singularity as quickly as they currently do. The equations are very complex (derived from a ...
7
votes
2answers
264 views

Solve a time-dependent matrix DE using NDSolve

I am trying to numerically solve a time-dependent matrix DE using Mathematica. However, it seems that Mathematica freezes even for two-dimensional matrix equations. For example, we have: ...
3
votes
0answers
94 views

Using NIntegrate and DiscretePlot to visualize pseudodifferential operators

In harmonic analysis, pseudodifferential operators are a way to generalize the notions of derivatives, through the use of Fourier transforms. The basic idea being, Let ...
1
vote
2answers
138 views

How to determine the parameter in a differential equation with some fixed solution

Assuming that I have a ODE system with undetermined parameter $$x''(t) == y(t) x(t)$$ $$y'(t) == 2 - a x(t)$$ and I have some fixed solution condition $$x(0)=0$$ $$x(10)=8$$ $$y(10)=3.5$$ Is there ...
2
votes
1answer
79 views

Using ouput of ParametericNDSolve as argument in NMinimize: NMinimize::nnum: function value not a number

I am trying to fit some experimental data and I am trying to use NMinimize function to calculate the parameters that fit the experimental dataset. I am also using ...
4
votes
1answer
169 views

EquationTrekker using Mathematica 10.2

I wonder whether the problem that arise with the following code is specific to my machine, as it seem to work with the documentation example. ...
3
votes
1answer
75 views

NDSolve: obtain time difference when different solutions get same distance to equilibrium value

I have a numerically solved a differential equation which has an equilibrium value and a starting point, both included as a parameter. I want to plot the difference between the times it takes to come ...
2
votes
1answer
124 views

Decouple 3 simultaneous 2nd order ODEs (of 3 dependent variables)

I have three simultaneous ODEs with coupled dependent variables. I was wondering whether there's a way for Mathematica to decouple these equations (into three ODEs of a single dependent variable ...
0
votes
0answers
185 views

How to solve the heat flow PDE for the constant source term

I have the two dimensional heat flow equation solved for a two dimensional reagion over time. That is an instance I found in the internet. What I am looking for is a method how to determine the heat ...
0
votes
2answers
166 views

How to solve this equation with NDSolve?

Here is the code: ...
0
votes
0answers
83 views

Piecewise NDSolveValue: Nested Variable Iteration

I am attempting to make the variable Rc a piecewise-function of [z] and have it update as NDsolve iterates through the range of 'z' such as {z,0,Le), but to no avail. The following code is an attempt ...
2
votes
1answer
86 views

Simplifying the result of DSolve

I have a system of differential equations that can be solved with DSolve. However, the coefficients are very long there are like terms which can be combined. I used //FullSimplify in my code but the ...
0
votes
1answer
133 views

Using NDSolve initial conditions as parameters for a function and then a replacement rule

I am trying to make a function based on two initial conditions of a set of differential equations: ...
12
votes
1answer
181 views

“ParametricSensitivity” in ParametricNDSolve

"ParametricSensitivity" is listed as a Method in the documentation for ParametricNDSolve, ...
1
vote
0answers
59 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 ...
2
votes
0answers
58 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
98 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
124 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
72 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
558 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
75 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
122 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
103 views

Getting the message NDSolve::underdet:

I am solving the wave equation with initial position and velocity function: ...
0
votes
1answer
68 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
226 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
39 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
178 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
142 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
225 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 ...
0
votes
2answers
134 views

Convert DE to first order?

I have the following set of second-order differential equations: ...