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

learn more… | top users | synonyms (3)

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
70 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
85 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
102 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
57 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
60 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
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
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
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
81 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
98 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
47 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
109 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
82 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
97 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
39 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
87 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
114 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
129 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
64 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
93 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 ...
1
vote
1answer
97 views

How many ODEs can NDSolve handle?

I am trying to simulate a coupled system of N blocks and springs. I am using NDSolve. For ...
5
votes
1answer
154 views

How to fit data to a convolution equation

How to fit data to a convolution equation: ...
0
votes
1answer
54 views

Maximum step size as a scalar function on the domain

In NDSolve when solving a system of ODEs, one can control the maximum time step for the whole domain with MaxStepSize. But there ...
1
vote
1answer
43 views

System of ODEs - NDSolve issues

I am a self-taught beginner trying to use Mathematica for the first time. If you wouldn't mind, I would like to ask for help with the code I am working on as I keep running into multiple issues when ...
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}) ...
1
vote
1answer
136 views

Strange WhenEvent Behavior

Given: ...
3
votes
1answer
59 views

DSolve with Piecewise Function in System of DEQs

I have been messing around with this problem from MSE, which is given by: $$ \ddot{x} = \begin{cases} -x + c\cdot \operatorname{sgn}(x)& |x| > c\\ 0 & |x|\leq c \end{cases} $$ where $c ...
4
votes
1answer
153 views

Solve motion from Hamilton's equations

I have a system of four coordinates and four momenta (conjugates of coordinates). I have a metric tensor $g_{ik}$ and I know the Hamiltonian: $H(p,q,t)=\frac{1}{2}g^{ik}(q)p_ip_k$ For my current ...
0
votes
1answer
76 views

Solving an equation and ODE simultaneously [closed]

I have a differential equation like $y'+a*y+b=0$. I have to find the value of $u=c*y+d$. These are the simplified form of the ODE and equation. Also, I have to plot $y$ and $u$ together.
2
votes
1answer
117 views

Problem with a plot for 1D wave equation solution using NDSolve [closed]

I can't properly use Manipulate for my solution of a wave equation. Can anyone help me? I have the wave equation in the form: ...
0
votes
0answers
64 views

Finding double inverse Laplace transform numerically

Edit: I asked Prof. Valko, he was so nice to point out where the mistake is. The problem is solved ! Thank you for your attention ! Recall the the double Laplace transform of a function $f(x,t)$ is ...
3
votes
1answer
87 views

Dsolve and Differential Equation for botnet defence

I am currently using Mathematica to solve $\frac{\mathrm{d}x(t) }{\mathrm{d} t} = cv_{H} (1-x) + \beta x(1-x) - (\gamma_{min} - v_{D}(\gamma_{max} - \gamma_{min}))x$ with $ x(0) = 0$. In the ...
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 ...
6
votes
2answers
94 views

inspecting step size and order of $\tt NDSolve$

I am trying to collect information about what step sizes and what orders is using NDSolve internally. I tried wrapping it into a ...