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

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1answer
862 views

Solving coupled eigenvalue differential equations [closed]

I am trying to solve an equation of the form as follows $\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\sin^{2}\left(z\right) & z\\ z & ...
2
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1answer
119 views

Differential Equation with Numerically Integrated Boundary Conditions

I have a second order differential equation that I'd like to solve numerically, and then integrate its solution twice to get the parametric equations of a curve. The ODE is: $2 ...
0
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0answers
45 views

How to numerically solve a Green's function using mathematica?

Suppose we have a Green's function $$LG(x)=\delta(x),$$ how to numerically solve it by mathematica? Can the mathematica read the delta function directly? For analytical calculation, we usually ...
0
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0answers
63 views

solving system of ODEs in Mathematica

I am using the DSolve to solve the following 2 ODEs \begin{equation} \begin{cases} &\dot{y}(t)=z(t)-y(t)-\frac{c_1c_2y(t)}{-c_1c_2e^{-t}t+c_1(1-c_2)+c_3e^{-t}}\\ ...
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0answers
27 views

Solving a set of differential equations with DSolve

I am trying to solve exactly a system of differential equations. The set of differential equations is given by : ...
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0answers
81 views

How to numerically solve this non-standard Green's function using mathematica?

$$\left(u(1-u^2)\frac{d^2}{du^2}-(u^2+1)\frac{d}{du}-\frac{au}{(1-u^2)}-\frac{bu^3}{(1-u^2)}+c\right)G(u,u')=mu^2\delta(u-u'),$$ where $a$, $b$, $c$, $m$ are constants, $u\in(-1,1)$ and the boundary ...
0
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0answers
56 views

Problem with piecewise function as source function of NDSolve

It seems that something wrong is with my piecewise source function u[t,x], so I get such an error: ...
0
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1answer
101 views

Solving this equation with NDSolve

I'm trying to solve a differential equation numerically. I've written this code but it is leading to some errors "initial history needs to be specified for all variables for delay-differential ...
0
votes
1answer
65 views

Function Evaluation in Table [closed]

Apologies in advance: this is a really basic question, and I am sure it has been answered, but I don't know enough mathematica to even find the answer. I have a differential equation I want to ...
0
votes
2answers
96 views

Solving recursion relation from power series

I am interested in solving differential equations in the form of power series. Let's say we have following equation: $$f^{\prime \prime} (\rho) + \left( \frac{2 e^{-k \rho}}{\rho} - \varepsilon ...
3
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0answers
126 views

Differential Geometry on a MeshRegion [closed]

NB- see this question for a more formal request. For many many years (honestly, since 1987) I've had my own MMa computational geometry code for dealing with 3D meshes. I principally (there's a joke ...
0
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2answers
79 views

Need to find value of NDSolve at specific value in range

I am working with NDSolve to plot an ODE as a function of time. I need to find a way to figure out the exact value X of the solution for some specific time, say t*. Even better, a way to figure out ...
0
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0answers
68 views

How to solve this PDE in mathematica?

I have been trying to solve this PDE, but Mathematica didn't give me a solution. Here it is: DSolve[{b*(-(3/2)*(9*Cos[[Theta]] + Cos[3 [Theta]])Csc[[Theta]]^7 D[h[[Theta], t], [Theta]] - (11 ...
1
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1answer
62 views

Differential equation [closed]

How does one solve this differential equation? $$y' = \frac{x^3 + 2x^2 y - y^3}{x^3 + x^2 y}$$
-1
votes
1answer
54 views

NDSolve and vectors [closed]

I think I can't find solution of equation below because I need use scalars, not vectors as I have tried. But I don't know how I can do express the problem with scalars. I have read Wolfram Language ...
2
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0answers
56 views

Solving a system of first order differential equations [closed]

I've got a set of equations of motion here (describing the interior of a charged black hole, if you're interested). It's just four first order ODEs, so Mathematica should be able to solve this easily ...
4
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1answer
89 views

Overriding default ExtrapolationHandler

When modeling systems with WhenEvent and NDSolve I found that the default extrapolation settings used in the returned ...
0
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0answers
34 views

Why differential equation reduces? [duplicate]

I am trying to ND-Solve the following equation: eqns = {x''[t] == -x[t], x'[0] == 0, x[0] == 4} The problem, is when I enter it, Mathematica reduces it to ...
0
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1answer
78 views

NDSolve for a system of nonlinear coupled pde

I try to solve a system($n$) of coupled nonlinear 1-d PDE's which is basically coupled sine-Gordon equations (through 2nd spatial derivative) in time and space. I am interested in the dynamics when I ...
5
votes
1answer
398 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
0
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1answer
57 views

Using DSolve for r(t) y'(t) = y(t) r'(t) [closed]

I am fairly new to Mathematica and I was trying to solve this equation r(t) y'(t) = y(t) r'(t) using DSolve. How can I adapt it to the DSolve function formalism?
0
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1answer
86 views

DEigensystem and NDEigensystem simply not working in Mathematica 10.0 [closed]

I am trying to use DEigensystem and NDEigensystem to check some theoretical derivations I have recently done. I am running ...
1
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0answers
93 views

How to find the eigenvalues of a custom operator using NDEigensystem? [closed]

I would like to solve a Hamiltonian presented by a 2x2 matrix. Hamiltonian is given by: ...
3
votes
1answer
125 views

how to speed up FEM-NDSolve for similar boundary conditions?

I need to solve several stoke's equations for very similar boundary conditions, which represent particles in a fluid with different velocities U[i]. I'm interested in computing the force acting on the ...
1
vote
2answers
127 views

How to plot coupled Differential equations with changing parameters?

I'm a new user of mathematica. What I'm trying to do is following: I have two coupled non-linear differential equations. Say $x'(t)$ = $A− (B +1)x + x^2 y$ $y'(t) = Bx − x^2 y$ What I want is to ...
2
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1answer
73 views

Heat transportation equation 2

I would like to thank you for all the suggestions for the problem with the heat transportation equation I have posted time ago! I rewrited the code along with the implementation of the Neumann ...
0
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1answer
118 views

Animate spherical pendulum

I want to plot the position of Spherical pendulum. First I tried to plot the simple pendulum: ...
3
votes
2answers
218 views

Is there is a decreasing function that fits my data?

Cross-posted in http://tieba.baidu.com/p/4440556337 http://tieba.baidu.com/p/4440547130 I was wondering if there is a function that fits the following data perfectly or properly. There is a ...
0
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0answers
46 views
1
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1answer
73 views

Numerical integration plot

I am trying to do a numerical integration plot in Mathematica. Specifically, I want to plot $r$ versus $\tau$ where, $$\frac{dr}{d\tau}=\sqrt{2F(r)}$$ $F$ being a quartic polynomial. The limit of $r$ ...
5
votes
1answer
85 views

Passing starting values to FindRoot when called by the Shooting Method of NDSolve

According to the documentation of the NDSolve Method -> "Shooting" option, it is possible to pass to ...
1
vote
1answer
83 views

Problem with Finding Minimum of a Function Solved With NDSolve

I am trying to find the minimum of a particular function, which is solved using NDSolve. What is making it a little more complicated is that it is not the only function solved within the NDSolve and ...
3
votes
2answers
90 views

Animating 3D Parametric Plot

I'm trying to create an animation of Lorenz equation as a function of t. Here is the numerical solution of the equation: ...
3
votes
3answers
162 views

Can I plot the solution to an ODE without using dsolve?

I have the following ODE $\qquad x'= -x^3+\sin(t)$ I want to find numerically the initial condition $x(0)$ corresponding to the $2\pi$ periodic solution. I tried to use ...
1
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0answers
52 views

NDSolve cannot consistently handle a simple 2D reaction-diffusion PDE with spiky (and random) initial conditions

I am still fighting with a modified version of the 2D reaction-diffusion PDE that I have already posted in a previous question ( Reaction-diffusion PDE with NDSolve: either very slow or very ...
0
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0answers
28 views

Use a Poincare map and Poincare section to show that the equation has a T-periodic solution [duplicate]

The equation is $x'(t)=-x(t)^3+h(t)$, where $h(t)$ is any smooth T-periodic function. Give an argument using a suitably constructed Poincare section/map that shows the equation has a T-periodic ...
6
votes
2answers
157 views

NDSolve and matrix formulation do not produce the same result. Why and which is more precise?

Let's assume a vector of variables $\vec a=(a_1(t),a_2(t),a_3(t))$ and let's assume a following DE$$C\ddot{\vec a}=B\dot{\vec a}+A\vec{a}+\vec F.$$ If $A$ and $C$ are both reversible, than the DE can ...
6
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0answers
212 views

Problems with NDSolve for solving coupled Schrödinger-like PDEs with perfectly matched layer boundary condition

I'm trying to solve a full-vectorial wave equation for an arbitrarily shaped wave guide, by using NDSolve and perfectly matched layer (PML) conditions. The PML ...
0
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1answer
40 views

DSolve “Equation or list of equations expected instead of True in the first \ argument ”

I am getting the error: Equation or list of equations expected instead of True in the first argument when I try to evaluate the cell. ...
2
votes
1answer
69 views

NeumannValue and FiniteElement Methods : BC not respected

I have noticed on several of my personal cases some issue with the BC using NeumannValue. Let me illustrate the problem. I take the 1D example of ...
2
votes
1answer
120 views

Improving the speed of evaluating numerical solution to a sytem of PDE

I am running a simulation for a kinetic reaction inside a pellet modeled by a system fo reaction-diffusion equations. ...
1
vote
1answer
47 views

Polar and Parametric Plots not showing up

I bet this has asked before, but I can't seem to find an answer anywhere. I have x and y functions which, individually plotted, are showing up fine, but when I try to plot the parametrically, the ...
1
vote
1answer
55 views

How to define “DiffusionCoefficients” in InitializePDECoefficients that depend on ElementMarker?

Modelling a Poisson Equation on piecewise constant material, ElementMarkers on the PointElements are used for the boundary ...
0
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1answer
54 views

NDSolve Unable to continue with complex values or beyond floating-point exceptions error

Initially tried to solve following first degree of differential equations using following method ...
0
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1answer
47 views

Failed to extract parameters by fitting data with ODE

I'm trying to extract 4 parameters by fitting one set of data with an ODE via NonlinearModelFit. I originally thought the process should be straightforward, but later on I found I was totally wrong. ...