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

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3answers
973 views

Solving One Equation with Two Variables

I am trying to solve an equation with two variables. It is the last step in the process of using the method of undetermined coefficients to solve a nonhomogeneous differential equation. The equation ...
1
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0answers
34 views

Determine Functions Given Data Points [duplicate]

Is it possible for Mathematica to solve for f(x,y) = 0 such that {x,y} contains {{0,0.5}, {1,0.5}, {0.6,0.8}, {0.4,0.2}} ? Do we need to specify f(x,y) first ? ...
0
votes
1answer
266 views

Solving a system of equations with variable coefficients

I am trying to solve a system of equation which seems to be simple but much as I tried I couldn't solve it in Mathematica and it says the coefficients need to be exact. Now, I was wondering if someone ...
1
vote
1answer
402 views

Finding solutions of polynomials system

Let $f_1,...,f_n$ be a set of polynomials in $x_1,...,x_n$ with rational coefficients. I need to check whether a system $$f_1=a_1,...,f_n=a_n$$ has a real solution for large enough count of points. ...
0
votes
2answers
486 views

find the real root

I have the following equation: \begin{equation} (y-1)^{b1} - C~~ y~~ \exp(a x)=0 \end{equation} where $a, b$ are real constants, $C$ may be a complex number. I need to find the real solution of the ...
-1
votes
2answers
95 views

single root of a cubic function

As it can be shown that the function f(x)=3x^3-9x+1 has a single root in the interval abierto (0,1). Try to solve using Newton Raphson method, but that is more than a demonstration calculation
1
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1answer
464 views

How to solve a complicated equation system

I am trying to solve the equation system eq1==eq2 for $\sigma1$ and $\sigma2$ where eq1 and ...
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 ...
0
votes
1answer
419 views

FindRoot finds a solution not found by NSolve

I am trying to solve a polynomial equation of higher order with non-integer exponents. When the order of the system is greater than 4, FindRoot provides a correct solution that is not found by NSolve. ...
4
votes
3answers
709 views

How can I find the boundary function in RegionPlot?

I have a problem with finding the function that gives the boundary curve in RegionPlot comamnd. I use the following code to make the regions in which two ...
1
vote
1answer
320 views

Numerical solution of two coupled transcendental equations with three variables

I have following set of coupled transcendental equations. $\tan^{-1} \left(\frac{\sigma+\beta}{K'-1}\right)+\tan^{-1} \left(\frac{\sigma-\beta}{K'-1}\right)=\frac{2 \sigma}{K'}\cos(\beta\tau)$ and ...
4
votes
1answer
259 views

Finding the roots of a function with a parameter

I am using a differential equation method for finding the roots of a function. My function is much more complicated but I can illustrate my problem with a trivial example. The problem occurs when ...
6
votes
2answers
453 views

Why does Equal[“string”, False] not evaluate to False?

Why does Equal["string", False] not evaluate to False? I would have thought Mathematica could prove that these two things are ...
3
votes
1answer
101 views
0
votes
1answer
132 views

Finding the first five eigenvectors and values for a 500×500 matrix

I'm trying to find the first five eigenvalues and vectors of a matrix that has the following proporties: ...
1
vote
0answers
135 views

Finding Values of All Nine Constants in q-hypergeometric Equation

I suspect that an identity of the form $$\sum_{j=-n}^{j=n}(-1)^jq^{j(5j+1)/2}=\sum_{r=0}^{n}f_{ar+bn+c}(-1)^{n-r}q^{(n-r)(dr+en+f)/2}\frac{(q;q)_{gr+hn+j}}{(q;q)_{n-r}}$$ for $a, \dots , j$ integer ...
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, ...
0
votes
1answer
214 views

Center Manifolds

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7
votes
2answers
233 views

How to correct this, `f[a_] := FindRoot[eq == 0, {x, 0.5}]`, where `eq` contains a parameter $a$, without using `eq[a]`?

I want to solve an equation with a parameter $a$, and define the result as a function of $a$. It is something like this: ...
2
votes
1answer
409 views

why doesn't NSolve find all the solutions that Solve finds?

Define d[p1_, p2_] := (p1 - p2).(p1 - p2) to be the square of the distance between two points. I am trying to solve equations like: ...
2
votes
2answers
177 views

Graphical solution of a a two-variable system containing an equation and an inequality

I'm currently studying atmospheric-gravity waves and their dispersion relations. I want to have look at values of $(x,y)$ that solve the following system : \begin{equation}\label{}(1) \left\{ \...
0
votes
0answers
128 views

Can't Solve a system of differential equations, Solve takes too long

My question is probably not really interesting but I really need help on this because I won't have access to a more powerful computer. So my model contains 7 equations : ...
1
vote
2answers
2k views

Solve within a range?

Is it possible to solve an equation in which some some of the parameters have defined ranges? Example: ...
1
vote
2answers
829 views

Projection of curve 3D (x,y,z) on the x-y plane

I have a following systeme : \begin{equation} \left\{ \begin{array}{rcr} (\beta+\frac{1}{2}\delta^{2})\nu_{1}(u)-\delta\nu_{2}(u)+\nu_{3}(u)& = &0\\ (\beta+\frac{1}{2}\delta^{2})\...
0
votes
1answer
100 views

RSolve works slow and does not give an analytical solution for solving high order linear difference equations

RSolve@@{{a[n]-a[n-10]==101}~Join~Table[a[i+1]==101+10i,{i,0,9}],a[n],n} I want to get the exact form of general formulas, but ...
0
votes
2answers
477 views

Symmetric function of the roots of a polynomial

First, I'm a beginner. I can compute the sum of roots with the follwing: Roots[x^7 + 5 x^6 + x^5 + x + 1 == 0, x] Plus @@ (x /. {ToRules[%]}) // Simplify Of ...
3
votes
3answers
239 views

Can Mathematica solve $x^{b^2} + ax^b -1 = 0$ for $x$ with $a>0$, $b>1$?

I have a problem that I can't seem to solve neither analytically nor with Mathematica. Namely, I have the expression $$x^{b^2} + ax^b - 1= 0,$$ which I want to solve for $x$ with $a>0$, $b>1$. ...
0
votes
1answer
416 views

Solve function doesn't work

I have the following system of equations that I need to solve: ...
0
votes
1answer
194 views

Nonlinear system of equations

I have been working to find an equilibrium solution for a Hamiltonian dynamical system. I have reduced the problem to the simultaneous solution of 3 equations: ...
0
votes
1answer
193 views
0
votes
1answer
122 views

NSolve cannot find the solution [closed]

I have some data which looks like: ...
0
votes
1answer
61 views

NSolve stalls when given an equation containing Log

Why does NSolve not work for this type of equation? ...
8
votes
2answers
259 views

What are the Method options Solve command accepts?

What are the Method options Solve command accepts? Solve has the Method option, however documentation contains no methods that it accepts...
3
votes
0answers
172 views

Solving Thue equations

A Thue equation is a 2-variable homogeneous integer polynomial of degree at least 3. It's well-known that such equations have only finitely many solutions over the integers. I'm trying to solve some ...
2
votes
1answer
97 views

Strange behavior using variable in Exists

I came across a behavior that doesn't make sense to me when I tried to use Exists in Reduce. If I run commands: ...
2
votes
3answers
501 views

Is there a way to specify custom domains?

I want to solve for all solutions to the system of equations $a_1 a_2 a_3 b_4 + a_1 a_2 b_3 + a_1 b_2 + b_1 = 0$ and $a_1 a_2 a_3 a_4 = 1$ where the $a_i$'s and $b_i$'s take on values from $\{-1,1\}$. ...
2
votes
1answer
115 views

Problem with SquareWave in NDSolve

I would like to have a triangulare signal drive a ODE system, using SquareWave[]. Something seems to go wrong though during integration. Uext'[t] and ...
4
votes
1answer
606 views

What algorithms does NSolve use?

I've been using NSolve to find roots and now I've been wondering what underlying algorithm Mathematica uses. It's probabaly similiar to ...
-2
votes
1answer
214 views

How to solve a non-linear equation?

I am trying to solve the following non-linear equation: $\frac{i e^{-x^2} \sqrt{\pi } x}{K^2}+\left(-0.131251-0.0379031 x^2-0.0151154 x^4-0.0100462 x^6+0.5 \left(0.00273859 +0.0400003 K^2\right) x^8+(...
0
votes
1answer
805 views

Solving a large system of non-linear equations

I am new to Mathematica, and I am currently trying to use it to solve a large symbolic system of non-linear equations. I began the code below about 30 hrs ago, and the Mathematica Kernal has been ...
3
votes
0answers
318 views

Function with a sharp resonance which Mathematica fails to integrate. Why?

I'm a new user of Mathematica and I'm trying to use it to calculate the collisional cross-section as a function of energy for a given potential and decay rate. I know that the resulting function ...
0
votes
0answers
43 views

Verify “Type” of solution [duplicate]

I've written some Mathematica functions which allow the user to verify if a mathematical function has certain properties. What I'm basically doing is generating "random" functions in respect of ...
0
votes
1answer
264 views

Notebook keeps running when Solve for variable

This might be a simple question for the most of you, but I am very new to mathematica so please bear with me. I'll refer to the code below: ...
4
votes
2answers
2k views

What is the efficient way to code Successive Over-relaxation (SOR) method in Mathematica?

I have written a SOR method (SOR is this method) code using C-style procedural loops. However, I think there might be (much) better ways to achieve the same end in Mma avoiding these loops. So my ...
1
vote
1answer
350 views

How can I find a root of my transcendental equation near a certain point?

What function could I use to solve this equation for x: E^(-x^2) = 1 - Cos[x] I tried Solve, ...
1
vote
0answers
27 views

Minimizing roots of a transcendental equations [duplicate]

I'm trying to use the solution of FindRoot with parameters for further calculations. Annoyingly enough it always gives me trouble with replacing the parameters. As an example I'm attaching a simple ...
0
votes
1answer
143 views

Two questions on strategies for quantifier elimination

With the help of people here I was able to solve several cases similar to IC3 but this case - unlike the other cases - does not return an answer. I will try to run it for a day with 8 processors but ...
11
votes
3answers
940 views

Finding “Maxima” and “Minima” on a B-Spline

I need to find the "Maxima" and "Minima" on a B-Spline or more correct the points where the 2nd components of the derivate equal zero. For example: ...