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

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2
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0answers
34 views
1
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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
109 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
139 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
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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 ...
8
votes
3answers
160 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
123 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
85 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
134 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
214 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
100 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
1answer
64 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
45 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
86 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}) ...
2
votes
1answer
196 views

Strange WhenEvent Behavior

Bug introduced in 10.3 or earlier and persisting through 10.3.1 or later Given: ...
3
votes
1answer
87 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
197 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
83 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
161 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: ...
3
votes
1answer
89 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 ...
5
votes
0answers
92 views

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

Bug persisting through 10.4. (windows 7, 64 bit) 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. ...
7
votes
2answers
121 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
107 views

Solving ODE system with NDSolve: “singularity or stiff system suspected” [closed]

I'm trying to solve a set of 4 ODEs as specified below, however I'm getting this error ...
1
vote
1answer
181 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, ...
14
votes
1answer
369 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
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1answer
83 views

singularity in boundary value problem

I am trying to solve a non linear differential equation with variable parameter. ...
3
votes
1answer
155 views

Finite Elements 3D

Does anyone knows how to solve the Laplace equation in a Sphere domain and with the following boundary conditions: Consider alpha=0. I have tryed the following code, but i don't belive the boundary ...
3
votes
0answers
113 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 $t(1,y)=y+2$? ...
1
vote
2answers
49 views

ParametricNDSolve and NDSolve inside Manipulate environment

I have a system of three coupled differential equations that can be pretty readily solved by NDSolve: ...
0
votes
0answers
60 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};}\\ ...
5
votes
2answers
107 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 ...
5
votes
2answers
111 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
172 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 ...
3
votes
1answer
44 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 ...
1
vote
1answer
157 views

Solving a system of partial differential equations consist of 6 equations on 9 variables by using Mathematica

I have a system of partial differential equations consist of 6 equations on 9 variables. ...
0
votes
1answer
122 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 ...
0
votes
0answers
24 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: ...
1
vote
0answers
99 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 ...
3
votes
1answer
68 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 ...
6
votes
2answers
311 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 $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
0
votes
0answers
22 views

Iterating with NDSolveValue in a Do-loop [duplicate]

I am trying to get a differential solution to converge. There are two separate time periods that I am solving for and the entire solution is periodic. I want to use the output from one as the input ...
0
votes
1answer
39 views

Error produced when trying to solve ordinary differential equation [closed]

NDSolve[{x0'[t] == -x0[t]*s*x1^2 + s*x1^2, x1'[t] == x1*s*x1^2, x2'[t] == -x2[t]*s*x1^2, x0[0] == x1[0] == x2[0] == 1}, {x0, x1, x2}, {t, 0, 1}]
3
votes
1answer
78 views

I Need help to solve the differential equation below

I tried to solve the equation using the code below, but got a null solution. If you change the values of p for 2 and alpha to -1.99, a smooth and nonzero solution is obtained. But I need to respect ...
0
votes
0answers
66 views

Loop Construct with NDSolveValue for Iterative Solution

I can get this code to run but the plots do not depict the solutions that are being evaluated inside of the Do loop. The plots are only showing the initial ...
1
vote
1answer
71 views

How can I combine NIntegrate with NDSolve?

I have no idea how to calculate the problems. For example consider following differential equation (DE): ...
4
votes
2answers
140 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 ...
0
votes
2answers
137 views

How can I perform NIntegrate with NDSolve?

I'm a new user and I have no idea how to perform NIntegrate by using NDSolve. For example consider following differential equation (DE): ...