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

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3
votes
1answer
93 views

How to determine the redundant equation in the set of DE?

my problem is messy, and I will use a simple problem to explain my problem. Suppose, we have a set of DE: ...
2
votes
1answer
75 views

Struggling with WhenEvent in NDSolve

I am doing some biological system modeling and trying to use WhenEvent in the initial conditions section of my NDSolve code to allow me to periodically change the value of a parameter (which I've ...
2
votes
1answer
159 views

NIntegrate::inumr: “The integrand `E^(-0.9τ1) DiracDelta[t-τ1] v[t-τ1] x[t-τ1]` has evaluated to non-numerical values ”

I am facing an interesting situation over here. The aim is to solve a system of IVP having an integral over a delay range. Here is my try ...
0
votes
0answers
53 views

ParametricPlot that worked in Mathematica 9 stops working in Mathematica 10

I've updated to Mathematica 10 and I am trying to plot the solution of a system of ODEs and I'm using exactly the same file that used to work in Mathematica 9, but now when I want to plot the solution ...
0
votes
0answers
66 views

Second Order ODE (Bessel Function) with a dependent variable in the BC

I have obtained an analytic solution to the following problem however I lack the knowledge to generate a numerical solution using mathematica. I'm reaching out to get an idea of what functions I may ...
3
votes
0answers
50 views

Does NDSolve automatically simplify the system of equations for Hermitian matices?

I am currently starting to solve numerically a system of differential equations like this: $\dot{A}(t)=S(A)A(t)$ Here, the matrices are of dimension $d\times d$. $S(A)$ is some superoperator that ...
2
votes
2answers
172 views

Strange behavior in ContourPlot?

I'm have a Abel's differential equation: ...
7
votes
2answers
223 views

How to locate the position of a periodic orbit

These are the equations of the dynamical system ...
1
vote
2answers
96 views

Can't NIntegrate my NDSolve results

I want to NIntegrate my NDSolve result. I don't have a exact function form because it is coming from the ...
9
votes
1answer
207 views

DSolve documention on web differs greatly from distributed MMA 10.2.0 version

In the course of improving my answer to 95361, I noticed that the DSolve documentation on the web is much better written than that distributed with Mathematica ...
3
votes
3answers
190 views

Trying to model a chemical reaction - NDSolve::litarg error

I am trying to model a chemical reaction with NDSolve. I have specified the known differential equations and parameters, ...
2
votes
2answers
160 views

DSolve gives an empty solution set to a solvable ODE

I really hope this isn't a duplicate, today I was answering this question and was to lazy to solve the quadratic equation on my own and so just asked mathematica to give me the solution of the ...
2
votes
3answers
467 views

Plotting a Bifurcation diagram

I have the following system equation v'(t)=2*G*J1[v(t-τ)]cos(w*τ)-v(t) How do you plot the bifurcation diagram, τ in the x ...
0
votes
0answers
39 views

Paramtric plot for 3 variable system

I have an system where I have calculated migration of "i" number of species "c" in "j" different habitats as a function of time. ...
2
votes
0answers
51 views

Numerical Analisys and StepDataPlot

I'm using StepDataPlot to compare several methods for differential equations. Does exists a function, or something else, to find the number of steps that the choosen method used to find the numerical ...
2
votes
1answer
57 views

WhenEvent stops working after first instance

I'm modelling a very simple physical situation is which an object is rested on two moving fingers. Sometimes the object moves with one finger while sliding over the other, while at other critical ...
2
votes
2answers
429 views

Plot Lorenz system

I solved the Lorenz system by using Euler forward method (without using NDSolve). But I am not getting the attractor. The Mathematica code is as follows ...
2
votes
2answers
108 views

Solving coupled ODEs with NDSolve to fit experimental data

I need to fit a multi-exponential data (Intensity x Time) using a model consisting of three differential equations. I want to find the parameters that gives the best fit to the experimental data. ...
0
votes
2answers
92 views

NDsolve complicated function

I'm trying to solve a complicated second-order ODE with NDSolve. I've never used NDSolve before. I've looked a lot of forums and tried some things, but I haven't been able to get the ODE's solution. ...
2
votes
1answer
85 views

Problems with multidimensional system of ODEs

I am trying to look at the migration of "i" number of species "c" in "10" number of habitats {designated as "j"} and to study their population size as a function of time "t". I have this following ...
0
votes
1answer
169 views

NDSolve::ndode: Input is not an ordinary differential equation [closed]

I am new to Mathematica. I am working on solving the following different equations numerically written in the code as below. ...
1
vote
1answer
115 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
vote
1answer
104 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
179 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 ...
2
votes
1answer
272 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
79 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
100 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 ...
3
votes
0answers
73 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
votes
1answer
101 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
vote
0answers
122 views

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

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= ...
1
vote
1answer
321 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
48 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 ...
1
vote
1answer
128 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 $(\sigma_{\ell},\mu_{\ell},d_{\ell},\sigma_M,\alpha_1,\beta,\alpha_2,\nu_M,\sigma_h,\nu_h,d_h)$: ...
0
votes
0answers
53 views

Using BSpline as initial condition in NDSolve [on hold]

I have not been successful in extending a 3D noise initial condition to a 2D situation. I would like to use a "noisy" initial condition to solve a non-linear PDE as shown. I used the following ...
0
votes
2answers
120 views

Why does Mathematica Hold my DSolve?

In one cell, I have ...
7
votes
1answer
193 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
185 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
120 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
226 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
92 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
368 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
182 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
162 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
87 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 ...