Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

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1answer
116 views

How do you solve a linear equation of matrices?

The function Solve works fine for scalars: In[]:= Solve[A x - x B + C == 0, x] Out[]= {{x -> -(C/(A - B))}} When using matrices however, ...
1
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3answers
224 views

Find all roots of a function with parabolic cylinder functions in a range of the variable

I want to find all roots of a function involving Parabolic Cylinder Functions. In what follows, I define 2 variables $\xi1$ and $\xi2$, which in turn depend on $\omega$. My function is then defined as ...
9
votes
1answer
154 views

NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity

I posted a similar question a short time ago regarding the 3D Coulomb problem. Jens' excellent answer to this thread allowed me to obtain the correct eigenvalues and eigenenergies for that system. I ...
8
votes
3answers
906 views

Implement the Bisection algorithm elegantly and easily

Description: Rencently, I have finished my course Numerical Analysis, so I'd like to implement many algorithm that I have learned from that course.By this practice, I hope that I can improve my ...
2
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0answers
61 views

Complicated implicit plotting - can it be tackled?

I'm quite new to Mathematica and have already spent tons of time on problems of this type, browsing through tutorials and topics here. I'm now coming to conclusion that it cannot be done and am about ...
1
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1answer
43 views

NRoots Results: From Equations to List of Root Values [on hold]

When I use Roots/NRoots, I get a disjunction of conditions as result. The conditions are normally of the type x == value How can I convert this to the list of root values?
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0answers
55 views
0
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0answers
40 views

NDSolve won't stop running [on hold]

I'm trying to solve the wave equation with NDSolve, but everytime I hit evaluate notebook it won't stop running. Any insights? ...
0
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1answer
75 views

How to find roots using the bisection method

First I plot the function and then I try to find a domain such that I can see the curve cut through the x-axis. I do this via trial and error ...
0
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0answers
32 views

Recycle boundary condition

I'm having the following issue that can not find a solution , by using this boundary condition u[0, t] == 2 u[1, t] that Mathematica does not understand, someone ...
3
votes
2answers
283 views

Roots of Whittaker W function

I am interested in finding the roots $u$ of the equation $$ W_{1,\imath b}(a)=0, $$ where $W_{\kappa,\mu}(z)$ denotes the Whittaker $W$ function, $a>0$ is a fixed parameter, $\imath=\sqrt{-1}$ and ...
1
vote
3answers
121 views

NSolve or Solve or FindRoot

I need to solve this equation: A == M/(f d/2 (1 + Sqrt[1 - 3.53 (M/(b d^2 c))])) to find M, with: A = 0 to 19635 for intervals of 5 f = 500 d = 100 to 500 ...
5
votes
2answers
148 views

NSolve behaving differently in V9, V10.3 and V10.4

EDIT In a very fast response from Wolfram they state that this is a known problem and give an example of it working for version 10.4.1. $Version "10.4.1 for Microsoft Windows (64-bit) (April ...
1
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1answer
188 views

Solving wave PDE

I am trying to solve the wave PDE with NDSolve. Below is the equation: ...
0
votes
2answers
77 views

Free-fall air resistance problem

I´m working on a free fall problem and I got an equation with variable $k$ when the situation has air resistance. Then I compared with no air resistance equation ($-4.9$, considering t variable). So, ...
0
votes
2answers
84 views

I'm trying to solve a system of complex equations

I'm simply trying to solve a system of equations and mathematica can't do it for all values over the region of interest. I have a 3x3 matrix that has a specific parametrization and after squaring the ...
1
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2answers
94 views

NSolve won't act on very large powers

I noticed that NSolve isn't running properly when I have some seemingly harmless numbers in my expression. Here is a simple example: ...
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0answers
74 views
7
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3answers
182 views

Find the number of $n$ such that $n!$ is a sum of three squares

I want to check the following theorem by using Mathematica: $\textbf{Theorem} $. $\text{The estimate}$ $\# \{n \le x:n! \text{ is a sum of three squares}\}=7x/8+O(x^{2/3})$ ...
0
votes
2answers
66 views

FindInstance function

I have a question concerning the FindInstance function. If I write FindInstance[c == 3, {c, l}] I obtain {{c -> 3, l -> 33/10 + (8 I)/5}} Is there any ...
4
votes
1answer
138 views

Verifying the outputs of 'Solve'

I got a solution for the equation ...
10
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1answer
181 views

NDEigensystem cannot solve numerically the 3D Coulomb problem, while DSolve returns the right answer

After having derived by hand the eigenvalues and eigenfunctions for the 3D and 2D hydrogen atom, I want to solve the systems numerically using Mathematica. I need to do this because my next step is to ...
1
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1answer
78 views

Solve does not seem to work for this equation

I need to solve the following equation, for which I am using Solve as below ...
-5
votes
1answer
33 views

Getting SetDelayed::error from Solve [closed]

I defied three functions as following: f1 = a1 x1 +a2 x2 + a3 x3 f2 = b1 x1 +b2 x2 + b3 x3 f3 = c1 x1 +c2 x2 + c3 x3 and I wrote ...
-1
votes
1answer
38 views

Solve returns empty list on system of 62 linear equations with undeclared known variables

Context: I am trying to solve a set of equations generated by hand from a complicated, but not particularly strange system via Newton's Second and Third Laws, and a few constraints. All the resulting ...
57
votes
9answers
3k views

Updating Wagon's FindAllCrossings2D[] function

Stan Wagon's Mathematica in Action (second edition; I haven't read the third edition and I'm hoping to eventually see it), demonstrates a nifty function called ...
1
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2answers
72 views

how to find sum of variable c1+c2+c3 for expression combinations

how to find sum of variable c1 + c2 + c3 for expression combinations: ...
3
votes
1answer
60 views

FindInstance only satisfies half of my double inequality

FindInstance[ 298973528525.436 < 10^10*(n - k*3.32192809488736) < 298973528539.862, {n, k}, Integers ] Result is: ...
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0answers
25 views

How to select one solution of a system? [duplicate]

The system, Solve[{F[x,y]==0,G[x,y]==0},{x,y}] has to solutions {{x->x0,y->y0}} How can I choose, for example, ...
1
vote
1answer
158 views

Why timing of FindRoot is almost the same even if the function is speedup significantly

This question is almost the same issue as this one. However, it seems that it didn't draw enough attention. Now I encountered the same problem. I previously make this post, I will copy the code here. ...
0
votes
1answer
75 views

How to plot a solution set? [duplicate]

I have two functions, let's call them $F1$ and $F2$. Both take the same three arguments: $x1, x2$ and $\epsilon$. With every $\epsilon^* \in [0,1]$, there should be either zero or one unique point ...
0
votes
2answers
104 views

Solve implicit system of equations

Hello everybody I try to solve this system of functions and try to plot it: x == 0.5(1.+Tanh[0.5*(x*y^2-eps1)/t] y == Tanh[(x^2*y+eps2)/t] with eps1 = 0. and ...
2
votes
2answers
69 views

How to Count the number of roots in the Domain from an equation

How do i Count[] the number of roots in the Domain and printout the intervals in x containing these roots. Given the function ...
0
votes
0answers
4 views

Finding multiples of three given a few simple rules [migrated]

We were given this problem the other day and it seems a little over my head, so I thought I'd share it here for any possible advice or assistance :). The problem is as follows: Initially, x = 1. For ...
3
votes
3answers
170 views

Cantor Pairing Function

I'm inspecting the Cantor pairing function, that we can find on this link here. But the strange thing is that Mathematica is outputting a wrong result to me. The code below shows the strange ...
1
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2answers
338 views

Solving pure functions

I've been trying to use Solve with pure functions to receive function efinition and then use it with Map , to obtain results from mapping function to some data. Here is example ...
0
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0answers
38 views

Nested system of equations [closed]

I was actually trying to do several functional ways of calculating matrices. The system is given in the figure \begin{align} \begin{pmatrix} \mathbf{p}_{1} \\ \mathbf{p}_{2} \\ \vdots \\ ...
2
votes
1answer
42 views

best way for finding approximate root of monotonic sawtooth like function

First I will generate such kind of monotonic sawtooth like function called func ...
1
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0answers
56 views

Reduce function with simultaneous equations and inequalities

I have some simultaneous equations that I want to solve, preferably analytically, yet I am unsure if the Reduce function is the correct route as it doesn't seem to ...
2
votes
1answer
94 views

Maximize a variable in NSolve Function

I want to solve a set of trigometric coupled equations with the NSolve funcion while at the same time trying to maximize a variable which has to be real and between ...
0
votes
1answer
61 views

Solve equation in a interval

I have a particle bouncing in a rigid box, my code is this: ...
0
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1answer
35 views

How can I set a solution of NSolve into the variable [duplicate]

I am trying to solve an equation such as: NSolve[Integrate[G[x], {x, -∞, ∞}] == 1 && B > 0, B] when ...
-7
votes
2answers
46 views

Solve using auxiliary variable [closed]

I can not think how to begin I need a help here please $x^{\log x}-x^{\log \frac{2}{x}}=1$
1
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1answer
82 views

Solve the interpolating function

I would have asked how to obtain the x given the y in an interpolating function, and I found the answer from here. But another question raised. I was dealing with measurement of the spectral ...
1
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2answers
39 views

how do I find the unknown coefficients of coupled equations

How do I find the unknown constants $x, y, z$ interms of a and b, using Mathematica. \begin{equation} \begin{split} 1&=-x+y+z \\ ...