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

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0
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1answer
216 views

How can I solve a 3D heat transfer partial differential equation? [closed]

It's a problem about heat transfer. Here is the equation : Is it solvable using this software? Edit Sorry, I'm new to Mathematica. I have the following code for this problem ...
0
votes
0answers
62 views

NDSolve::bcedge error when solving PDE on a square region

I am solving a 2D PDE system: ...
2
votes
1answer
104 views

FindRoot of interpolating function from NDSolve

I am having issues finding the root of an interpolating function obtained from NDSolve. For example: ...
0
votes
3answers
72 views

How to select coefficient of an exponential function

Suppose I have these set of equations: sol = DSolve[{ x'[t] == -RandomReal[]*x[t] + y[t], y'[t] == x[t] - *y[t] , x[0] == 1, y[0] == 0}, {x[t], y[t]}, t] The ...
1
vote
0answers
102 views

Numerically Solving Helmholtz over the Rectangle - Why does this code only give eigenfunctions of the form $u_{m1}$ [closed]

I have been following the method for numerically solving the Helmholtz equation in this example (the answer by User21) and have come across two problems. I have been implementing the method for a 2x1 ...
0
votes
1answer
133 views

Solving quantum harmonic oscillator in 1D for a displacement of the ground state as initial state [NDSolve]

As an exercise, I want to numerically solve the quantum harmonic oscillator in 1D. ...
6
votes
1answer
163 views

NDEigensystem producing imaginary eigenfrequencies for the vibrations of a cantilever [closed]

We are trying to use NDEigensystem to solve for the vibrational modes of a cantilever with triangular cross-section. However, many of the solutions provided by NDEigensystem have imaginary ...
3
votes
2answers
69 views

Assigning multiple solutions different replacement names

Let's say we are solving a homogeneous differential equation, such as $$y^{\prime\prime} + a y^{\prime} + b y = 0$$ with characteristic equation $$s^2 + a s+ b = 0.$$ Using the ...
5
votes
2answers
175 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: ...
8
votes
1answer
182 views

Bug? Problem with derivative of interpolating function from FEM

Bug introduced in 10 or earlier and fixed in version 10.4 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 partial ...
0
votes
1answer
73 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
48 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
64 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 ...
6
votes
2answers
191 views
0
votes
1answer
77 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. ...
7
votes
0answers
422 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
1answer
72 views

Paramter Scans and $\chi^2$ Test in Mathematica

Is there any in-built function or a recommended package that enables one to find, say, 10 Parameters, which are used as boundary conditions in NDSolve, that minimize $\chi^2$? ...
1
vote
2answers
99 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
44 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
37 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: ...
1
vote
1answer
177 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
88 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 ...
8
votes
1answer
69 views

Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
0
votes
0answers
47 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 ...
8
votes
1answer
146 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
106 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
63 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
142 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
66 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
233 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
231 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 ...
1
vote
1answer
80 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
30 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
107 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
120 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
69 views

Simple Neumann condition over rectangle

have some problem with Neumann boundary conditions over simple rectangle. Here my code ...
1
vote
1answer
130 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 ...
0
votes
0answers
54 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
59 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
128 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
166 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
199 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 ...
12
votes
1answer
198 views

How to enforce a symmetric solution with FEM?

I'm solving the laplace equation in a domain with holes, and I need to compute the integral of the gradient on the boundary of these holes. For that I define a mesh and solve the laplace equation ...
2
votes
0answers
34 views
1
vote
1answer
111 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
44 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
111 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
167 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
43 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
129 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 ...