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

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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 ...
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 ...
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). ...
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 ...
5
votes
3answers
507 views

Plotting the direction field of a differential equation

I have to sketch the direction field for the following differential equation: $$\frac{dy}{dx}=\frac{-0.02 y +0.00002 xy}{0.08 x-0.001xy}$$ This is the code I used, which gives an incorrect plot: ...
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 ...
3
votes
2answers
251 views

How to propel the integration of time a little bit further? Numerical solution can not evolve to the max time

I try to solve a nonlinear partial differential equation. I obtain a numerical solution which can not continue to the max time I set, I always receive message NDSolve::ndcf: Repeated convergence ...
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 ...
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 ...
3
votes
1answer
164 views

Extracting data from NDSolve result

Normally I wouldn't ask such question before even read the material from the Wolfram Documentation about what I'm trying to do but this time I have a pretty tigh dead end. I apologize for that. So, ...
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: ...
4
votes
1answer
152 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 ...
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 ...
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.
1
vote
0answers
169 views

Help with calculating a complicated integral

Edit: The question is solved : )) Thank you for your attention ! I am sorry for mass questions, but the question bothers me a lot. So I would like to ask this question here. This problem arises when ...
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 ...
1
vote
1answer
149 views
-3
votes
1answer
223 views

system of differential equations in Mathematica

How can I formulate the addressed system of differential equations in Mathematica for to find a general solution for $f[x_1, x_2, x_3, y_1, y_2, y_3]$. ...
7
votes
0answers
516 views

Modelling Hysteresis with a Differential Equation

I want to implement the bulk ferromagnetic hysteresis model (mostly the Jiles-Atherton Model), see http://drum.lib.umd.edu/bitstream/1903/6043/1/PhD_99-1.pdf page 44 equation (30). The needed ...
0
votes
1answer
98 views
14
votes
1answer
260 views

Stress calculations using finite elements

A standard engineering problem is to calculate stresses in a structure due to applied forces. With the inclusion of the finite element method in version 10 this question attempts to investigate how ...
1
vote
1answer
294 views

How can I use Mathematica to solve a Stefan Problem using an explicit scheme?

I would like to plot the temperature distribution for a particular case. the problem is stated in the paper, behind a paywall here, summarized as Consider a one-dimensional container of length l, ...
1
vote
1answer
70 views

singularity in boundary value problem

I am trying to solve a non linear differential equation with variable parameter. ...
2
votes
1answer
69 views

FiniteDifferenceDerivative of complex function in 2D--bug?

I want to compute partial derivatives of complex functions via finite difference approximation on two dimensional grid using NDsolve`FiniteDifferenceDerivative ...
3
votes
0answers
96 views

How to solve partial differential equation

How to solve in Mathematica this partial differential equation: $0.5\frac{\partial t(x,y)}{\partial x}+1.5\frac{\partial t(x,y)}{\partial y}+t(x,y)=y\cdot \sqrt{1+x^{3}}$ with condition $t(1,y)=y+2$? ...
5
votes
2answers
104 views

To solve an ode system with pulses

I want to solve an ode system with pulses, for example x'[t] == b*(1 - x[t]) - a*x[t]*y[t], y'[t] == a*x[t]*y[t] - d*y[t] in {t,0,1} and then at the end of ...
1
vote
2answers
43 views

ParametricNDSolve and NDSolve inside Manipulate environment

I have a system of three coupled differential equations that can be pretty readily solved by NDSolve: ...
6
votes
1answer
811 views
0
votes
0answers
57 views

singularity problem in mathematica [duplicate]

$$ \pmb{\beta [\text{b$\_$},\text{c$\_$}]=\frac{4 c-14}{12 b-6 c-9};}\\ \pmb{\alpha [\text{b$\_$},\text{c$\_$}]=\frac{10-4 b}{12 b-6 c-9};}\\ ...
20
votes
2answers
394 views

Getting rid of spikes in the PDE solution

Bug introduced in 10.0 and fixed in 10.3 Note: In 10.0, Rationalize[fd, 0] was needed or mesh generation would fail. Preamble: I am solving a PDE in a domain ...
6
votes
2answers
302 views

Kernel quits without error in NDSolveValue

The crash is fixed in version 10.3 I am using the latest 10.1. The following single line command makes the kernel quit without error message (just a beep): ...
6
votes
1answer
162 views

Long running ToElementMesh with very “large” domains

This is fixed in version 10.3. I'm trying to solve a system of PDE over a large domain. This doesn't means I need to have a huge amount of mesh points and mesh elements to discretize the domain. ...
4
votes
2answers
130 views

Solving parametric ODEs at large parameter values

Question 101668 was not particularly clear and was put on hold for that reason. The author did clarify it a bit, but it seems unlikely that the question will be reopened. Through an exchange of ...
5
votes
2answers
95 views

NDSolve divide-by-zero trouble

So I have a set of differential equations (which I know are analytically integrable) but I want to integrate them numerically to get the form of the solution (the solution is not explicit and hence I ...
1
vote
0answers
75 views

How to make a parameter stochastic in a differential equation system with NDSolve?

I constructed the differential equation system below, which I solved using NDSolve. Now I need one parameter ($mu$) to be stochastic, e.g. Poisson distributed around a mean and changing slightly at ...
5
votes
2answers
283 views

Inverse Laplace transform

Let $r=\mu = 0.15; \sigma = 0.05; T = 1; S_0 = 100; K = 95;$ Let $\nu:=\frac{2\mu}{\sigma^2}-1$ and $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
7
votes
3answers
193 views

Vector form using NDSolve

Michael E2 wrote a wonderful solution for my question. Now I am considering the system: $$ \begin{align*} x'&=x^2 y,\ x(0)=1\\ y'&=-x y^2,\ y(0)=1 \end{align*} $$ I am wondering how I can ...
3
votes
1answer
35 views

solving large number of linear differential equations

I want to solve a large system of 500 by 500 differential equations such that I have equations such as: Note all the A1, A2 are ...
0
votes
1answer
112 views

how to write this equation In mathematica. where is W is random value either 0 or 1

how to write this equation In mathematica. where is W is random value either 0 or 1. i want to run to certain N=100 I already have ...
1
vote
0answers
75 views

Coupled ODEs with boundary conditions - DSolve Error [closed]

I'm relatively new to mathematica and I can't find the error here. I suspect it has something to do with the fact that vx, vy, vz aren't blue on my mathematica - as in, they already have some assigned ...
6
votes
2answers
2k views

Error entering equation in DSolve

I entered a command incorrectly as follows: DSolve[{y'[x]=y[x]},y[x],x] I am now experiencing: ...
0
votes
1answer
122 views

Solving systems of equations and derivatives

I am new to Mathematica, and I'm not sure how to solve a system of equations that include differentiation. Given that f and g are differentiable functions: ...
0
votes
0answers
22 views

How to use `DSolve` with y'' and y' in the same argument? [duplicate]

I'd like to solve the differential equation $y''(x)=xy'(x)$ in Mathematica. I'm not sure if it can be solved analytically. This is what I have tried: ...
0
votes
0answers
462 views

Poincare Section of an Hamiltonian

I'm in desire to plot the Poincare Section of a differential equation defined by a hamiltonian system. The hamiltonian is as follow: ...
0
votes
0answers
191 views

How can one use differential boundary conditions with helmholzSolve?

I can not get the helmholzSolve function provided by Mark McClure and user21 to work for a case that I want to constrain the spacial derivative of a boundary. In ...
3
votes
1answer
65 views

Find an appropriate algorithm for certain type of first order nonlinear PDE

I am trying to solve a first-order nonlinear PDE of the form $$ \partial_t z(t,x) = f(t, x, z(t,x), \partial_x z(t,x)) $$ with the boundary condition $$ z(0,x) = \phi(x) $$ for some finite domain $x ...