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

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1
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1answer
129 views

DSolve gives no output

I have troubles finding a solution to a system of three coupled nonlinear ODEs. When I put it into Mathematica, I get back the input as an answer. Could anyone tell me what I'm doing wrong? Here is ...
1
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1answer
107 views

Singularity problem of a 2nd order differential equation

I would greatly appreciate your help in implementation of Mathematica for solving a 2nd order differential equation expressing some important engineering problem. Apparently, this equation has no ...
5
votes
3answers
181 views

How to change symbols in differential equation with a single rule?

Problem Suppose I have a differential equation such as $\qquad f'(x)+f(x)=0$ and I want to change it into $\qquad y'+y=0$ My Method Using rule = f[x] -> y,...
2
votes
1answer
293 views

Heat transportation equation

I have a problem with the solution of the heat transportation partial differential equation in cylindric coordinates. Basically I have to numerically solve the equation for a pipe through wich the ...
2
votes
1answer
83 views

how to write generic equation for Recurring differential equations?

Hi I am a biologist and I want to model some ecological data that I have. I am new to mathematics and to ODEs. I want to write generic equations for a multi-dimensional system of ODEs. So, I want to ...
0
votes
1answer
115 views

Problem in solving a simple Laplace equation

I am trying to solve the following Laplace PDE in MMA: $$\frac{\partial^2 T}{\partial x^2}+\frac{\partial^2 T}{\partial z^2}=0$$ subject to the boundary conditions: $$\frac{\partial T}{\partial z}|_{...
3
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0answers
80 views

Diagonalisation of equations for NDSolve

I have a linear matrix differential equation and I wish to speed up evaluation by diagonalising using eigenvectors. There is an example in Help for finite elements under "swinging beam" that is ...
0
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1answer
112 views

Solving of three non-linear simultaneous differential equations with given boundary conditions

I am trying to solve three simultaneous differential equations in Mathematica-10 but I am not able to get the solutions. After running the following command as I am pressing shift+enter it just simply ...
1
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0answers
134 views

How to write code for solving a second order differential equation? [closed]

I am new to Mathematica and am trying to figure out how to solve the following second order partial differential equation using DSolve. $\qquad U C_{x}+V C_y= C_{...
1
vote
1answer
367 views

How can I use Mathematica to solve a Stefan Problem using an explicit scheme?

I would like to plot the temperature distribution for a particular case. the problem is stated in the paper, behind a paywall here, summarized as Consider a one-dimensional container of length l, ...
0
votes
1answer
50 views

Checking the solution of a differential equation with a boundary condition depending on an arbitrary function

I have the partial differential equation: $\qquad U_{x} - 4 x^{2} U_{t} = x U, \qquad U(x,0)=f(x), \qquad x \in (- \infty, \infty), \qquad t \in (0, \infty)$ Where $U_{x} = \frac{\partial U}{\...
1
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1answer
143 views

Finding equilibria to a system of 3 ODEs with 11 unknown parameters. Looking for the intersection of 3 surfaces

I have the following system of 3 ODEs of 3 variables $(\ell,M,h)$ and 11 parameters $(\sigma_{\ell},\mu_{\ell},d_{\ell},\sigma_M,\alpha_1,\beta,\alpha_2,\nu_M,\sigma_h,\nu_h,d_h)$: $\frac{d\ell}{...
0
votes
2answers
128 views

Why does Mathematica Hold my DSolve?

In one cell, I have ...
7
votes
1answer
200 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
119 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
208 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
131 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
237 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
97 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
197 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
395 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
391 views

Time evolution of a bispinor [duplicate]

The effective Hamiltonian for polariton graphene is given by: ...
5
votes
1answer
155 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
222 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
170 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
94 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
739 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
154 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
147 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
61 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
141 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
355 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: $$\frac{d}...
3
votes
0answers
98 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 $u(x)\in\mathcal{S}(\mathbb{R}^...
1
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2answers
141 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
94 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
180 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
79 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
132 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 each),...
0
votes
0answers
192 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
175 views

How to solve this equation with NDSolve?

Here is the code: ...
0
votes
0answers
84 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
162 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
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: ...