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
221 views

Periodic boundary condition

I want to solve a PDE as: $\frac{\partial u}{\partial t}=\frac{\partial u}{\partial x}$, with conditions: $u(x,0)=sin(\pi cos(x))$ and $u(x+2\pi,t)=u(x,t)$. I have solved it by hand and obtained: $u(...
0
votes
1answer
74 views

Can I tell DSolve to solve a first-order ODE by method of separation of variables?

I meet a first-order ODE $$\frac{dy}{dt}=\frac{a(\ln\frac{1-c}{1-y})^3}{\frac{b-y}{1-y}+\ln\frac{1-c}{1-y}},$$ where $a,b,c$ are constants. The ODE is subjected to the initial condition $y(t=0)=y_0$. ...
0
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0answers
91 views

How to solve boundary value problem with singularities at boundaries?

I have a boundary value problem, solving a system of differential equations with a singular boundary condtion (V[0] = 1/s, s->0) ...
5
votes
3answers
213 views

If statement within WhenEvent

I'm trying to integrate an equation with a periodic solution using NDsolve. I want to stop the integration after the derivative of my solution has become zero for ...
2
votes
1answer
111 views

Boundary condition not fully taken into account in DEigensystem?

Context Mathematica 10.3 now has the very nice DEigensystem function. ...
3
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2answers
420 views

Solve stiff system by shooting method

I'm trying to solve a second order differential equation with the shooting method but, it appears to be a stiff system. This is worst for a larger parameter $\mu$. I've tried different methods: ...
10
votes
3answers
523 views

Trying to find the asymptote to a function

I am trying to find the asymptote to a solution of a differential equation. I solved $x'(t) = \sin(x(t) + t)$ using NDSolve and plotted my solution. ...
1
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0answers
51 views

Combining Manipulate and NDEigenvalues [closed]

I think there may be a quick solution to this problem which I can't seem to fix at the moment. The question is how do we eliminate the error in the following ...
1
vote
1answer
117 views

NDSolve : Second order ODE with variable coefficients

I have a second order ODE of the form : u''[x]+ p[x]u'[x]+ q[x] u[x]==0 ; with, ...
3
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4answers
208 views

Finding the “least” singular solution for NDSolve

I need to solve a ODE for a function $f_\sigma(x)$, where $\sigma$ is a free parameter to tune. All the solutions are supposed to be singular for some value of $x$, except one for a given value $\...
3
votes
1answer
84 views

Need help understanding the output of `DSolve`

I give Mathematica 10 the following command: DSolve[I D[P[x], {x, 2}] f[x] - (P'[x])^2 f[x] + 2 I P'[x] f'[x] == 0, P, x] and I have the following output: ...
1
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1answer
103 views

How can I handle interface thermal boundary conditions?

I am trying to solve a system of PDE´s coupled by interface boundary conditions, this is my code: ...
1
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2answers
99 views

Evaluation to true using DSolve - syntax errors?

Probably a stupid question, apologies, but I am getting an annoying error when I try to evaluate the following simple PDE $\frac{\partial C}{\partial t} = d \frac{\partial^2C}{\partial x^2}$ between $...
0
votes
0answers
32 views

StreamPlot, ListStreamPlot does not visualize vector field properly [duplicate]

I am reopening my question about empty stream plots. I couldn't find a choice for parameters that would give me a proper stream plot for the following example. ...
0
votes
2answers
114 views

How to display results of NDSolve

I am solving differential equation of second order ...
1
vote
2answers
179 views

StreamPlot, ListStreamPlot scaling issue [duplicate]

The following stream plot is empty and the x-axis exceeds $[-0.1,0.1]$ significantly. StreamPlot[{y, -100000 x - y}, {x, -0.1, 0.1}, {y, -100, 100}] Using ...
1
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0answers
55 views

Solving a 4th order PDE (Plate bending) [duplicate]

I'm trying to solve the following PDE but I'm getting this error. The PDE represents the bending of a thin plate. ...
2
votes
2answers
241 views

Attempting to use NDSolve to plot harmonic oscillator solutions

NDSolve[{ (-y''[r]/1880) + (470 (0.04077)^2 r^2 - 48 + 1/(1880 r^2)) y[r] == 0, y[0] = 0, y'[0] = 0}, y, {r, -4, 4}] I use this but get errors and am ...
1
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2answers
61 views

Plotting issue for nonlinear de

The following code with varying scaling parameter gives same plot. plz suggest correction. ...
2
votes
1answer
97 views

Singularity while solving PDE

I have to solve a PDE (in the context of the functional renormalization group in physics). I have a function of two variables, $U(l,p)$. I know $U(0,p)=U_0(p)$ and then I have an equation (eq925) that ...
0
votes
1answer
116 views

How to solve this DE?

The previous plot has executed. I have another code. This neither shows error nor shows any plot. ...
1
vote
2answers
122 views

Error NDSolve::nlnum1 from 2nd order ODE with 4 boundary conditions

I want to solve this 2nd order ODE with two initial conditions close to the origin (one to the function and the other to its derivative) and more two similar conditions for an endpoint. ...
7
votes
2answers
160 views

Unexpected warning from DSolve

I'm trying to solve this differential equation with respect to $x$ $$ \frac{d^2y}{dx^2}-\bigg(\frac{dy}{dx}\bigg)^2-\frac{1}{x}\frac{dy}{dx}=\frac{1}{x^2} $$ With boundary condition $y(1)=2, y'(1)=-...
0
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2answers
182 views

Solving non-linear differential equation

For my research project I need to solve the following integral ...
0
votes
1answer
110 views

FM NMOR in Cesium with Atomic Density Matrix package [closed]

I am trying to use the atomic density matrix package in Mathematica to simulate FM NMOR in Cesium. The example given in the package is for a specific system from J=1 to J'=0. I am trying to simulate ...
3
votes
1answer
94 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
104 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
180 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
55 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
68 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
52 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
175 views

Strange behavior in ContourPlot?

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

How to locate the position of a periodic orbit

These are the equations of the dynamical system ...
1
vote
2answers
120 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 ...
10
votes
1answer
213 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 10.2....
4
votes
4answers
262 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
176 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
543 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
41 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
53 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
60 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
470 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
123 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
95 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
222 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
136 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
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
182 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
308 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 ...