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

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12
votes
1answer
138 views

Strange result of Reduce and ForAll

In the question Can Mathematica tell me if a polynomial has all real roots?, quite a few of interesting answers were given. I wanted to add another one, using quantors, and observed some strange ...
9
votes
2answers
5k views

Inverse of a complicated function

Mathematica is struggling to find the inverse of this function f(r): ...
6
votes
1answer
253 views
5
votes
1answer
408 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 ...
4
votes
1answer
761 views

How do I use RSolve to solve a system of recurrence relations?

I am trying to solve a system of recurrence relations as follows. ...
3
votes
2answers
4k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
3
votes
1answer
800 views

Solving Simultaneous Equations

I am trying to solve two equations that take the form: $W_0 \sqrt{1+\left(\dfrac{z}{\lambda\,\pi\, W_{0}^2}\right)}=W_1\;\,\quad \ldots(1)$ $W_0\sqrt{1+\left( \dfrac{z+0.1}{\lambda\, \pi\, W_{...
3
votes
1answer
2k views

NDSolve does not respond

For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
1
vote
1answer
781 views

Using previous two solutions as a start point in FindRoot

I need to solve a sequence of equations and I want the starting point of each new FindRoot to be the solution of the earlier FindRoot, increased or decreased by a a bit in the following way: Some ...
1
vote
3answers
459 views

Solve simple trig equation

I would like to solve this equation: $$-x\sin(x)=\cos(x)$$ But Solve in Mathematica doesn't work: This system cannot be solved with the methods available to ...
0
votes
1answer
492 views

How to use `FindRoot` to solve an equation containing a parameter?

I'm trying to derive some of the results of the following paper: Electrodynamics of semiconductor-coated noble metal nanoshells, JT Manassah - Physical Review A In the paper there is matrix $\mathbf ...
8
votes
2answers
1k views

Find the parameter values satisfying conditions for all roots of an equation

Hi I'm very new at Mathematica. My real problems concerns a much more difficult equation with many parameters, but I want to check that the method is good, so I made up a test equation. My test ...
7
votes
2answers
3k views

Finding y given x from an interpolating function

I would like to put a dot on the point of a curve that has a specific y value but I don't know the x value. A simple example of my code is ...
5
votes
2answers
886 views

Methods for NSolve

I've been using NSolve a moderate (50-100 equations) size system of linear equations and it has been working splendidly (Solve ...
5
votes
2answers
377 views

Why doesn't Roots work on a certain quartic polynomial equation?

In everything that follows I am using Roots to get the solutions to the equations. I start off with this equation: $$ \frac{A}{3}x^4 - x^2 + 2ax - b^2 = 0$$ Now ...
4
votes
3answers
254 views

Why the inequality does not take into account the domain?

I have this inequality: Reduce[(4000-1000k)/(k-4) < 0] and the answer is k ∈ Reals I would expect ...
4
votes
2answers
333 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 $...
4
votes
4answers
171 views

Implicit function theorem to higher order

Consider f[x_, y_] := Csc[0.482` y] Sin[0.963` x - 0.482` y] + 3.247` Csc[0.333` y] Sin[0.667` x - 0.333` y] + 5.049` Csc[0.119 y] Sin[0.238 x - 0.119 y] I'...
3
votes
3answers
242 views

Speed up Eliminate

I have a set of trig equations, c1,c2,c3 are constants, I excepted the result is c1 c2 c3 r^2 + (c1^2 + c2^2 + c3^2 - 1) r + c1 c2 c3 == 0 but following code ...
3
votes
1answer
205 views

Strange behavior of Reduce with a cubic equation

This equation: $(\frac{-a}{x})^2=\sqrt{\frac{1}{x}}$ at $a > 0$ and $x > 0$ has a clear solution $x=a^{4/3}$, doesn't it? However, ...
3
votes
1answer
76 views

Using result of Solve in further calculations

I'm trying to make a code for Gauss-Legendre quadrature. First I find the roots of the polyinomial with roots[n_,x_]:=Solve[LegendreP[n, x] == 0] Then I need to ...
3
votes
3answers
1k views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
3
votes
1answer
96 views

Unable to solve equation for a variable by any method

I am looking to solve for the value of r when the derivative of the expression ...
2
votes
1answer
186 views

How to properly interpret a seemingly contradictory result in Mathematica?

I have a problem with interpreting the results of my notebook outputs. It is important that I do not err with the interpretation. Here is the full input: ...
2
votes
2answers
395 views

NSolve for high degree univariate polynomials

I am trying to solve a high degree univariate polynomial using Mathematica's NSolve command. But when I plug the solutions generated by Mathematica back to the equations, the equations are massive ...
2
votes
1answer
745 views

How to guess initial complex value for FindRoot

I have to solve a transcendental equation for a parameter, say $\beta$. Now, the $\beta$ has a range from $ik$ to $k$ where $i$ is the usual imaginary root $\sqrt{-1}$ and $k$ is a real number. ...
2
votes
3answers
541 views

Points of Intersection

How to numerically find points of intersection between pair of curves (Here,a circle and a parabola) ? Finding it a bit messy as, for a point on one curve, slope of the other is involved. ...
2
votes
1answer
126 views

Undershoot/Overshoot Method for this differential equation?

I have tried to solve this equation for some weeks and I am not capable. I have read in articles that it is easy with an undershoot/overshoot method, but I don't know how to do it. $y''+\frac{3}{x}y'-...
1
vote
1answer
120 views

How to speed or help Solve[] when it is stuck?

The code below generates a system of equations that I need to Solve[] for {c[5], c[6], c[7], c[8]} in terms of {c[1], c[2], c[3], c[4]}. ...
1
vote
3answers
251 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 ...
1
vote
3answers
159 views

automatic processing of numerical results in `Plot`

First I want to solve an equation $F(x,y)=0$ for $y$ by supplying a value of $x$. (suppose obtaining the analytic form of $y(x)$ is too difficult) Then I want to plot root $y$ (numerically calculated) ...
1
vote
2answers
306 views

Mathematica can't minimize a function

Mathematica seems not to be able to minimize this univariate function over integer arguments, $r>2, r \in \mathbb{Z}$. ...
1
vote
2answers
469 views

solving for one solution to a system of polynomials

I'm trying to solve a system of equations: ...
1
vote
1answer
126 views

Applying N to the roots found by Solve gives complex numbers when the roots are real [closed]

I have a function which is f(x) = x^3 - 5 x^2 - x + 1. When I solve for x to find the zeros ...
1
vote
1answer
216 views

Solving systems of equations

So I have a set of equations like 12 of them but 13 variables. However I would like to find the numerical value of the roots for the maximum value of a particular variable. I don't know how to do that ...
1
vote
2answers
294 views

Is there a better way to get the eight points of intersection?

I want to get the eight points of intersection from the equations 2 Abs[x] + Abs[y] == 1 and Abs[x] + 2 Abs[y] == 1. To solve ...
1
vote
1answer
1k views

This system cannot be solved with the methods available to solve

I know questions about this warning have been posted a thousand times over. But I really couldn't find any solution that worked in my case. It's quite simple: ...
0
votes
1answer
216 views
0
votes
2answers
112 views

Finding all complex polynomial roots in a specified range efficiently

I need to find the roots of a rational polynomial that are near i. In the following code, I try that two different ways. First, I use a constraint to only find roots in the right region. Second, I ...
0
votes
1answer
159 views

How to solve this nonlinear 2 by 2 equations?

I have a equation (x^2 + q1^2 - y^2)/2*(x + q1 - y) + (1 - 2*a)*q + 2*F = 2*(1 - a)*c[q] in q(variable) with parameters q1,a,F and function c(in variable q also, and I define it outside Solve so I can ...
0
votes
6answers
260 views

Roots of a characteristic equation. Can Mathematica solve it?

I have been using Mathematica for a few years, but with basic things. Now I need to find the first 10 roots of the following equation: ...
0
votes
1answer
144 views

More issues Integrate, NIntegrate, FindRoot

I'm trying to solve a system of 3 non-linear equations using FindRoot and Integrate. If I start FindRoot[] close to the right answer, it works well but returns a bunch of error messages first. ...
-2
votes
1answer
96 views

Solve For X inside arc-cos function (with division) [closed]

Very basic but I've been stuck for more than 12 hours trying to solver this equation 20=360/(arccos(X/3200)*2) Can anyone solve X? and explain what exactly you ...
15
votes
2answers
4k views

FindRoot Domain restriction

I am solving a system of four non-linear equations in four variables using FindRoot. I have some sense of the relationship between the variables so I don't want Mathematica to do its computations in ...
23
votes
2answers
1k views

Using the Krylov method for Solve: Speeding up a SparseArray calculation

I'm trying to implement this Total Variation Regularized Numerical Differentiation (TVDiff) code in MMA (which I found through this SO answer): essentially I want to differentiate noisy data. The full ...
22
votes
4answers
1k views

Hightlight all the self-intersections of a Lissajous figure

This graph–also known as a Lissajous figure–contains so many self-intersections.How can I highlight them? ...
17
votes
1answer
1k views

Is Mathematica `ContourPlot` function really so efficient?

I wanted to find the roots of the function $f(x,y)=\sin(3.2x)\sin(1.3y)-2.1 \sin(1.3x)\sin(3.2y)$. This is what the function looks like: ...
16
votes
1answer
2k views

What are the algorithm details of FindRoot?

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system". But I ...