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

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1
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1answer
231 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 ...
2
votes
1answer
181 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
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2answers
376 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
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1answer
99 views
0
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1answer
127 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: ...
0
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0answers
80 views

System of differential equations - solving for a constant

I will reformulate my question in the hopes it will be more intelligible. First, I defined the functions: ...
1
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0answers
123 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
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1answer
193 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
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1answer
202 views

Center Manifolds

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7
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2answers
198 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
216 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
139 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
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0answers
80 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
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2answers
943 views

Solve within a range?

Is it possible to solve an equation in which some some of the parameters have defined ranges? Example: ...
1
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2answers
510 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\\ ...
0
votes
1answer
94 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
241 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
221 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
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0answers
220 views

Solve function doesn't work

I have the following system of equations that I need to solve: ...
0
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1answer
172 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
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1answer
147 views
0
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1answer
97 views

NSolve cannot find the solution

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

NSolve stalls when given an equation containing Log

Why does NSolve not work for this type of equation? ...
6
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2answers
186 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
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0answers
148 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
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1answer
87 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
271 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 $\{-1,1\}$. ...
0
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0answers
135 views

NDSolve producing an overdetermined system

I am trying to build the initial model for an electro-mechanical system that I will be running in a for-loop for various inputs and parameters. Currently, the code is as follows: ...
2
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1answer
94 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 ...
2
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1answer
404 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 ...
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1answer
192 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) ...
0
votes
1answer
551 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 ...
0
votes
0answers
65 views

Using NSolve in a function, selecting one indexed result and using it to plot another function containing a function containing the indexed result

I have a problem using the result pcvar[g] g e (0,1) in the plot cvar1. In the plot cvar I can use it. It must be somehow connected to clearing p in the definition of pcvar[g]. I am gratefull for any ...
3
votes
0answers
284 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
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1answer
150 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
946 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
237 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
26 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
128 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 ...
10
votes
3answers
754 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: ...
1
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0answers
34 views

Correct use of Mathlink's MLGetRealList

I am attempting to use Mathlink from C. I have managed to return single values from mathlink to my c program, but I am having trouble with lists. Consider the Mathematica operation: ...
2
votes
0answers
613 views

FindRoot in range

I am trying to find all roots in a range, using y /. FindRoot[Sin[y] == 0, {y, #}] & /@ Range[7] which gives ...
4
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3answers
381 views

Finding parameters making real part of eigenvalues vanish

I have the following $\;3\times3$ matrix: $\left( \begin{array}{ccc} 0.04 -0.4 b & 0 & 0.04 -0.4 b \\ 0 & -0.08-1.2 b & -0.06-0.9 b \\ 1.04 -0.4 b & 2.08 -0.8 b & 0 ...
0
votes
1answer
57 views

Help with Reduce, quadratic system of inequalities

I'm trying to obtain an equivalent system of inequalities to the one below but without the variables x and z. Somehow Reduce just repeats the command. ...
0
votes
4answers
154 views

RSolve fails on a two-equation non-linear system

I have a system of just two recurrence equations, I need to solve them and so I use RSolve: ...
1
vote
1answer
332 views

Why my differential equations become True? [duplicate]

I've been trying to solve a system of nonlinear differential equation, but the conditions are a bit weird. Two of the differentials equate to the same equation, but have different boundary ...
1
vote
1answer
263 views

Get Cos[2 x] in “Solve”

My goal is to get an analytical solution of x ( $\lambda$ in the problem), when $\epsilon$ (f[x] in the problem) is maximum (use inverse form). I found that if I can use trigonometric identity ...
0
votes
1answer
103 views

Equation in implicit form

This is simple example: v = {1.48622576, 1.53444276, 1.42299438} v/(v + 1) Out[1]:= {0.597784, 0.605436, 0.587288} In the above case expression v/(v + 1) is ...