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

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5
votes
2answers
168 views

Trying to simulate pulse width modulation

I am trying to simulate a pulse width modulated signal in a NDSolve, but i have a hard time passing the signal function in. This is my code: ...
7
votes
1answer
110 views

Bug? Problem with derivative of interpolating function from FEM

Bug introduced in 10 or earlier and persists through 10.3.1 I am really not sure if this is a bug or I am missing something very trivial. QUESTION: What I am missing in order to obtain the ...
0
votes
1answer
54 views

How to plot dy/dx and y together for a differential equation? [duplicate]

For the differential equation y'(x)+a*y(x)=d, how to plot y'(x) and y(x) for given values ...
0
votes
1answer
47 views

Problem in trying to solve a differential equation [closed]

I'm trying to solve a differential equation but not getting a solution. Some references I read gave me hits about using a runge kutta method. I'm new to the software, any hints regarding this error ...
0
votes
0answers
60 views

Help numerically solve this non-linear PDE with singularity

I have trouble finding a numerical solution to the partial differential equation below. It seems to be a singularity in the solution somewhere, so I searched online and found that it is suggested to ...
5
votes
2answers
147 views
0
votes
0answers
44 views

Getting NDSolve::conarg: error from attempt to solve diffusion equation

I'm trying to model diffusion of a single species from a fixed reservoir into a porous solid. Function u[x,t] should go from 0 < x < L, while f[x,t] should go from L < x < Vratio. I have ...
0
votes
1answer
72 views

Differential equations expressed in operator form [duplicate]

Is it possible to make a workable operator representation of differential equations in Mathematica? I think it would make solving my differential equations easier, but I have no idea how to do it. ...
0
votes
0answers
46 views

Implement Lagrange Multiplier in NDSolve

I have a Lagrange function $L$ that depends on a couple of complex, time dependent coefficients $A_{\alpha,j,n}$ where $\alpha \in \lbrace{1,2\rbrace}$, $j,n \in \lbrace{1,\ldots,N\rbrace}$ where $N$ ...
0
votes
0answers
90 views

How to Plot a 4D PDE

I have a PDE within 4 parameters u[x,y,z,t], now I want to plot this in a cube. the equation is: ...
7
votes
0answers
343 views

Problems when solving a nonlinear PDE system with NDSolve

The nonlinear PDE system is actually extracted from a research paper published in 2000 Here is the paper link The authors solved the system by using an ordinary differential equation integrator in ...
1
vote
2answers
85 views

Bessel-like equation problem with NDSolve

I am trying to solve the following nonlinear ODE, but Mathematica takes forever to give a result. Any idea why? ...
1
vote
1answer
38 views

Differential equation for a list with parameter dependent function

I am having a differential equation: y' = (1 - y) - f[y, mu] y; f is a hysteretic function that depends on y and on the derivative of y: ...
0
votes
0answers
35 views

Recursions where one definition depends on another. How to Block or have local variables?

I have been using Mathematica to solve a second order differential equation using the second order Verlet method. My code looks like: ...
0
votes
1answer
94 views

Laplace Transform of a Multidimensional Partial Differential Equation

I'm trying to use Mathematica to solve a multidimensional partial differential equation using Laplace tranforms. The PDE is as follows: $$ \frac{{\partial T}}{{\partial t}} = \frac{{{\partial ...
3
votes
2answers
77 views

track equilibrium of periodic ode system

I am trying to track equilibium in a periodid ode system. In such systems the equiblirium is defined as x[t]=x[t-1] and ...
-2
votes
0answers
76 views

singularity or stiff system

I have tried to solve this rotating disk flow problem in Mathematica. However, I got errors. Why did Mathematica return this error, mind to explain and help me solving this kind of error? ...
6
votes
0answers
47 views

Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
0
votes
0answers
32 views

Combining two NDsolves results in “The search has encountered a complex value…” and no solution

So far I used to seperate NDsolves to solve a system of coupled differential equations, where the first NDsolve yields the Boundary conditions for the second NDsolve ...
3
votes
0answers
86 views

Constructing the coefficient matrix in discretization of a PDE

In order to solve the following two dimensional PDE $$\frac{\partial u(x,y,t)}{\partial t}-\frac{1}{2} \sigma _1^2 x^2 \frac{\partial ^2u(x,y,t)}{\partial x\, \partial x}-\frac{1}{2} \sigma _2^2 y^2 ...
8
votes
1answer
103 views

NDSolve`FiniteDifferenceDerivative gives wrong result when the precision is not MachinePrecision

Bug introduced in 8 or earlier and persists through 10.3.1 I want to get a pseudospectral differentiation matrix by NDSolve`FiniteDifferenceDerivative. ...
1
vote
1answer
70 views

Meniscus outside of a cylinder - axisymmetric Young-Laplace equation in semi-infinite domain

How to solve the axisymmetric Young-Laplace equation $$\frac{z'(r)}{r \sqrt{z'(r)^2+1}}+\frac{z''(r)}{\left(z'(r)^2+1\right)^{3/2}}=z(r)$$ with b.c.s $$z'(1)=-2$$$$z'(\infty)=0$$ where $z=Z/l_c$ ...
0
votes
0answers
58 views

Eliminating one function from non-linear PDE

Is there any solution to eliminate function p[x,y] from these two equations which are equal to zero (diff1=0 and diff2=0) where c and d are constants. I need one equation where should figure just ...
6
votes
0answers
125 views

Heat convection differential equations from 1952 - Mathematica “fails to converge”

I am trying to solve a fundamental problem in analytical convective heat transfer: laminar free convection flow and heat transfer from a flat plate parallel to the direction of the generating body ...
0
votes
0answers
61 views

Solving Coupled Differential Equation to Get Smooth Asymptotic Solution

I'm trying to solve these differential equations. I want to use Mathematica 9 to solve this system of equations but I still can't do this simply. This is the system of equations: ...
5
votes
1answer
169 views

Trouble with shooting method for a 4th-order stiff ODE

The ODE I need to solve is $$\left(y^3y^{\prime\prime\prime}\right)^\prime+\frac{5}{8}xy^\prime-\frac{1}{2}y+\frac{c}{y}=0$$ where $\prime$ denotes differentiation, $c$ is a constant and ...
1
vote
2answers
219 views

Problem solving a second-order PDE

I am looking for numerical solutions for a class of equations of the type : e = Derivative[2,0][ps][x,w]+(2/x)*Derivative[1,0][ps][x,w]-r[x,w]==0 With r a ...
0
votes
1answer
49 views

DSolve - Complex Number Solutions

some of you know that I have been working on my dissertation of Game-Theoretic Modelling of Cybersecurity (Thank you again to everyone who has helped me with Mathematica so far). The differential ...
0
votes
1answer
29 views

Compute StateResponse for list of inputs

How do I find the state response of a system for a list of inputs? Simply writing an array in the place where the input enters as an argument of StateResponse ...
0
votes
0answers
82 views

Plot of 4-dimensional vector field

I want to study a certain type of 4-dimensional ordinary differential equation. How could I visualize it? One thing that could be helpful is to plot the vector field in one pair of variables, for a ...
3
votes
0answers
99 views

Hopf Bifurcation for a non-linear dynamical system [closed]

I am very new to mathematica and also to Hopf bifurcation or any bifurcation for that matter. But I am trying to obtain a Hopf bifurcation for a dynamical system. Now, so far, I cannot find any ...
0
votes
1answer
56 views

Simple Neumann condition over rectangle

have some problem with Neumann boundary conditions over simple rectangle. Here my code ...
1
vote
1answer
58 views

Differential Equations and Unit Notation

What do I get the Syntax::sntxi: Incomplete expression; more input is needed . error when I try to use the math palette for derivatives? What does the dot in 10. Farad Micro Volt mean? ...
0
votes
0answers
49 views

DSolve DAE echoing - no solution/response

I am aware that there are lots of questions about this topic but they are all slightly different. I am attempting to program a cybersecurity infection model and there are 4 states that a computer can ...
2
votes
1answer
57 views

NDSolve with minimum value [closed]

I want to plot the decay of $O_3$ to $O_2$. My system and my code (x = $O_3$, y = $O_2$): ...
4
votes
0answers
111 views

new kernel crashes using DSolve in 10.3.1

Update: I added small movie showing the crash, since others who tried it so far could not reproduce it on their system. Original question I am finding new problems with ...
0
votes
0answers
83 views

Bifurcation diagram and Poincare section of the Damped Forced Pendulum

First, I want to make the bifurcation diagram of the damped forced pendulum. To this end I used the following code: ...
6
votes
1answer
168 views

Trouble with shooting method for a 4th-order differential equation

I'm trying to solve the following forth-order ODE with the shooting method: $$\frac{1}{5}(y-2xy^\prime)=\frac{1}{x}\left\{\frac{xy^\prime}{y}+xy^3 \left[\frac{(xy^\prime)^\prime}{x} \right]^\prime ...
2
votes
0answers
28 views
1
vote
1answer
98 views

Integration of Frenet-Serret differential equations [duplicate]

Are there programs available in Mathematica or other related sources where third order Frenet-Serret equations are numerically integrated to find coordinates in 3-space? Curvature/torsion given as ...
0
votes
0answers
40 views

implicit solution to PDE with strange return type

I want to solve the following PDE eqn = D[q[k, t], t] + \[Alpha] (1 - q[k, t]) D[q[k, t], k] == q[k, t] (q[k, t]-1) for $q(k,t)$. The solution that is returned ...
3
votes
1answer
93 views

Finite Difference - heat generation in a square (square within a square)

I am trying to develop a code that will allow me to solve the following problem. Lets say that I have a square block, inside that square block I have a smaller square box thats at a certain ...
1
vote
1answer
92 views

Differential equation in two variables

I have a system of second order differential equations, with two independent variables, which represents a trajectory. I tried solving this system using NDSolve and ...
0
votes
0answers
37 views

DSolve doesn't give an output for a system of ODEs

I'm trying to solve a system of four ODEs. However, DSolve doesn't give any output (no mistake either). ...
8
votes
1answer
115 views

What should I learn from DSolve working better with a named constant than a number in this case?

I have an equation $$\bigl(r''(\phi)r(\phi) - r'(\phi)^2\bigr)\bigl(b + r(\phi)\bigr) = r(\phi)\bigl(r'(\phi)^2 + r(\phi)^2\bigr)$$ Here $b$ and $r$ are lengths, and $\phi$ is an angle (in radians, so ...
7
votes
3answers
130 views

DSolve—different solutions for same set of equations using different symbols?

I happen to find that DSolve can give different solutions, even a different number of solutions, for a set of differential equations just by making a change in the ...
1
vote
1answer
109 views

How to creat mesh on the cube's surface?

Now I'm trying to solve a PDE by FEM, and I need creat the 2D mesh on the cube's surface, the figrue below shows my idea. Both the quadrilateral elements and triangle element are OK. I read the ...
0
votes
0answers
65 views

Solving system of Fredholm integral equations of the second kind

How can we generalize the code previously introduced to solve the Fredholm equation of the second kind to the case of a system of Fredholm integral equations of the second kind? $$ ...
1
vote
1answer
95 views

System of Four First Order Equations for Double Pendulum using RK-4 - Code Improvements

I have spent quite a bit of time implementing the double pendulum equations at the bottom of this web site using Runge-Kutta-4. I am also quite aware of the built-in Runge-Kutta methods, but I need ...
5
votes
2answers
204 views

Solve numerical differential equations at `t->Infinity`

I have a first order non-homogeneous system of differential equation (100+ equations, so no hope to solve them analytically, due to the Abel–Ruffini theorem). If I solve them using ...