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

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0
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3answers
61 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 ...
2
votes
1answer
58 views

FindRoot of interpolating function from NDSolve

I am having issues finding the root of an interpolating function obtained from NDSolve. For example: ...
7
votes
1answer
109 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 ...
6
votes
1answer
131 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 ...
0
votes
1answer
57 views
1
vote
0answers
74 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
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 ...
5
votes
2answers
3k views

How do I plot a solution of a differential equation?

I am having trouble generating a plot for a solution to my differential equations. I always end up with just blank axes. ...
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: ...
3
votes
2answers
65 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 ...
2
votes
1answer
214 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 ...
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 ...
2
votes
1answer
136 views

Getting errors NDSolve::nlnum, NDSolve::icfail)

I would like to plot the function v[r], and resolve this differential equation in spherical simmetry: ...
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 ...
9
votes
2answers
3k views

Is it possible to do vector calculus in Mathematica?

I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components ...
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
43 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
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 $N$ ...
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? ...
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: ...
5
votes
1answer
168 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
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 ...
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
74 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 ...
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 ...
6
votes
0answers
47 views

Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
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 ...
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: ...
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
1answer
48 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
83 views

Solution of differential equation using other differential equation

I have a differential equation $y'(t)+2a\sqrt{e+y(t)+1}=h-2a$ where $e,h$ and $a$ are constants with the terminal condition $y(T)=0$; $T$ may be 10 or 12... etc. And $x'(t)+(a/\sqrt{e+y(t)+1}) ...
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 ...
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 ...
0
votes
1answer
56 views

Simple Neumann condition over rectangle

have some problem with Neumann boundary conditions over simple rectangle. Here my code ...
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 ...
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
55 views

Getting Data from Differential Equation Solution

I am solving the following differential equation. I need to get the values of y[x] for x ranging from 1 to 30. I need to get ...
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 = $O_2$): ...
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 ...
4
votes
0answers
78 views

unhandled win32 exception in WolframKernel.exe in DSolve of non-linear ODE in one variable

Installed 10.3.1 and started to run some old ode's. in V 9, this ode used to return unsolved, which is ok, but in 10.3.1 now the kernel crashes. This is on windows 7, 64 bits. I wonder if this also ...
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: ...