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

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0
votes
2answers
59 views

Using result of Solve as plot parameter [closed]

Recently I have faced a problem I would appreciate it, if you helped me I have the following code in Mathematica I want to plot a function let say z * 10 * t where <...
1
vote
1answer
45 views

How to define a Reduce function in order to define two parameters afterwards

I'm trying to evaluate numerically an equilibrium for a system of ODEs: dA = c A + b B - a A dB = d B + a A - b B So I define a list of known parameters: ...
3
votes
1answer
64 views

Solve with Reals gives different answer

I'm very new to Mathematica (started using ver 10.4) and I was just verifying my calculations. I have the following equation: ...
0
votes
1answer
71 views

Solution for Imaginary part of equation

I have a function Il12i[-0.001, -0.001, w, 0, 1, 0, 0.1002] which is depends on 1 variable w and it is real if w > -3666 (this number I found from graphs). This function is very complicated numerical ...
1
vote
1answer
59 views

Testing equivalence of analytical expressions like $x^2 -x == x(x-1)$

On occasion I have two expressions that I may be equal but simplified differently, and I want to check if they are actually equivalent. Using the equation in the title, $x^2 -x == x(x-1)$, sometimes ...
0
votes
1answer
550 views

Problem with FindRoot applied to functions

I am having difficulty with the error "is not a list of numbers with dimensions..." when using FindRoot (and other numerical routines in Mathematica) to solve equations numerically when the argument ...
0
votes
2answers
52 views

Solving several inequalities in Mathematica

I am a very beginner of Mathematica and the following will probably be a very stupid question. I have a bunch of inequalities in 6 unknowns and I want to find the set of values satisfying them. Can I ...
0
votes
2answers
76 views

FindInstance is very slow on an apparently simple problem

I wish to use FindInstance to find a set of solutions of this problem: ...
4
votes
2answers
841 views

Solving a linear equation in Mathematica

This should be easy but I can't seem to find the right way to do it. I have an equation of the form $a x + b x + c y + a z + d z = 0$, and I'd like to solve for relations between the parameters $a,b,...
6
votes
2answers
274 views

Find a condition that b must satisfy so that Ax=b has solution

I'm new to Mathematica, so I'm sorry if this is really simple. I am trying to find the condition that vector b must satisfy so that Ax=b has solution. I would like to learn a general method, but I'll ...
1
vote
1answer
241 views

Why Integral does not converge?

I am trying to solve for $\Omega$ this nonlinear integral equation: $$1+\dfrac{z}{k^2}-\dfrac{z^2}{K_2(z)} \dfrac{\Omega}{k^3} \displaystyle\int_{1}^{\infty} \gamma^2\, \text{ArcTanh} \left(\sqrt{\...
0
votes
1answer
49 views

Errors only when code is iterated

Hello I'm trying to have two for loops sweep two parameters and for each 2-tuple of those parameters I want to solve a differential equation. To do this I have the following code: ...
4
votes
4answers
185 views

Solving Recurrence Equation $a_{n+1}=a_n(1-a_n)$

How to solve following recurrence equation $$a_0=2$$ $$a_{n+1}=a_n(1-a_n)$$ I tried: ...
0
votes
1answer
53 views

Reduce unable to solve simple inequalities with quantifiers

I have try to solve following inequalities using Mamthematica. But it unable to solve that. ...
0
votes
0answers
30 views

Finding results using qualifiers?

I have set of recursive function definitions and assumptions $\forall n.t1(n+1)=t1(n)-Y*S(n)$ $\forall n.t2(n+1)=t2(n)+S(n)$ and assumption $\forall n.n<K\rightarrow L1=L2*t2(n)+t1(n)$ I want ...
5
votes
1answer
1k views

How to take the derivative w.r.t. an arbitrary function?

EDIT: The answer posted by @Jens works for built-in functions only. However I'm starting to wonder if this is related to my Mathematica install somehow. I have version 7. Here is an example in the ...
1
vote
1answer
79 views

Solving two equations with modified Bessel functions

I am trying to solve two equations with Bessel functions in them, 1) C1*BesselK[0, 3.7268*10^-4*x] == 1.3*10^-6 2) ...
2
votes
1answer
55 views

Substituting values of variables in solution of a system of linear equations

After solving a system of 21 linear equations in 21 variables (called Xi in my code) I got the values for all the 21 variables, in the following way: ...
3
votes
1answer
81 views

Solve equation for a function as solution

I need to solve the following function: $$ h(z) = \sum^{40}_{k=0} \frac{k \, p(k)}{z- k \, h(z)} $$ where $p(k)$ is a probability distribution (in this case binomial with n = 40). Note that $h(z)$ is ...
0
votes
1answer
56 views

Arranging sides of an equation [duplicate]

I have to create my own function to solve equations (first and second degree). Assuming you have any input equation, how can I do to bring everything to the first side of the equation? Example. I ...
0
votes
0answers
38 views

Matrix with equations as entries - how to choose them and solve them

I have a matrix in Mathematica, which I have built using Normal[SparseArray]. Each entry of this matrix is an equation in one variable. What I need to do is 1) to select some of the entries of the ...
0
votes
1answer
36 views

Parameterize Subset of Complicated Zero Set

I recently asked this question: Evaluating Functions on Zero Sets (of other functions), and got fantastic assistance, but realized that there seems to be an extra issue when you're trying to ...
0
votes
0answers
26 views

Using the “reduce” function with s lot of equations and inequalities

I am using "reduce" to obtain all positive integers (plus 0) which satisfy a group of equations and inequalities. I have to automatize this procedure because I have to use "reduce" with at least 100 ...
3
votes
2answers
109 views

Evaluating Functions on Zero Sets (of other functions)

I have a highly non-trivial function, call it $f(x,y)$, in which I want to look at its zero set in the $(x,y)$ plane, and plot/evaluate a different function $g$ precisely along this zero set. I have ...
1
vote
2answers
131 views

Find all the non-negative integer solutions of a linear equation

For the linear equation x[1] + x[2] + x[3] + x[4] + x[5] == n Is there any efficient way to find all the non-negative integer solutions of this equation when n ...
0
votes
1answer
87 views

Solve equation with two different sets of replacement rules

I want to solve eqn for c0 in the following code. I want to do it with both replacement rules. I realize I could just use solve ...
0
votes
3answers
86 views

Interactive Application using Manipulate for Fibonacci Series

I am working on creating interactive app using Manipulate function on fibonacci series using SeriesCoefficient. I want to plot the fibonacci numbers based on the slider of Manipulate function. I have:...
14
votes
3answers
6k views

Solving a time-dependent Schrödinger equation

I want to solve the time-dependent Schrödinger equation: $$ i\partial_t \psi(t) = H(t)\psi(t)$$ for matrix, time-dependent $H(t)$ and vector $\psi$. What is an efficient way of doing this so that ...
5
votes
0answers
51 views

Is there a way to tell how much time FindRoot is spending calculating Jacobians? [closed]

I am solving a large number of trascendental equations by scanning FindRoot over a bunch of seeds and a bunch of different parameter values, and I would like to ...
12
votes
3answers
292 views

Archimedes' Scheme to find $\pi$

Given an Archimedes' scheme $$a_{n+1}=\frac{2a_nb_n}{a_n+b_n}$$ $$b_{n+1}=\sqrt{a_{n+1}b_n}$$ with initial values $a_0=2\sqrt{3},b_0=3.$ How do I prove using Mathematica that this converges to $\...
19
votes
1answer
309 views

Can Mathematica solve functional equations with nested variable?

First, inline free form input can solve these equations: But it seems no native Mathematica function can solve these, there is even an error page for equations of this form (nestdv). Now my ...
1
vote
3answers
158 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 ...
0
votes
0answers
28 views

Question about # Symbol [duplicate]

I am trying to solve an equation and the solution includes # symbols. I read up on them but can't understand how they are related to my solution. I solved a simple trigonometric equation of third ...
15
votes
2answers
1k views

Getting an InterpolatingFunction from a ContourPlot

I have a function, say minimizeme[Ω_][β_][ϵ_] = ϵ^2 Ω - Log[2 (Cosh[2 β] + Cosh[2 β ϵ])]/(2 β); I want to find its critical points in $\epsilon$ for a given ...
1
vote
1answer
81 views

Finding roots of Bessel function $y=3J_1(x)+xJ_1'(x)$ is returning inaccurate roots. Not Kernel bug [closed]

I can't figure out why Mathematica is returning the incorrect roots. The first five should be 2.9496,5.84113,8.87273,11,9561, and 15.0624 according to my textbook. ...
2
votes
2answers
70 views

How to find intersection points of linear and semi-logarithmic plots

Hopefully the title depicts what I am trying to do. Below is a figure of my calculations that is shown in logarithmic scale in the x-axis. I am trying to find a way to find the intersection point at ...
2
votes
1answer
63 views

Solving a big number of non linear equations

I have three trapezoids. The first sharing its upper side (I will call b_{i+1} in the code) with the second, the third sharing its lower side with the upper side of the second. All shared sides are ...
0
votes
0answers
36 views

How to speed up Solve command in Mathematica 8.0?

I have two complicated mathematical functions $f(s)$ and $g(M)$ that are complicated functions of $s$ and $M$ respectively. I would like to solve the equation $f(s)=g(M)$ in order to plot $s$ vs. $M$. ...
1
vote
1answer
67 views

Using NSolve for Elliptic Equations over Fundamental Parallelogram in Complex Plane [closed]

I'm considering solving elliptic functions over a fundamental domain of the torus with half-periods $\omega_{1}=\pi/2$ and $\omega_{2} = \pi \tau /2$, where $\tau$ is the modular parameter of the ...
0
votes
2answers
66 views

Unable to plot function with exponentials or to find all roots [duplicate]

I am not able to Plot[(-1)^x + 2^x - 2 x - 1, {x, -4, 4}] directly. Some rework might be needed with complex branch cuts perhaps. There are real roots at $ x=3, ...
0
votes
1answer
122 views

NSolve takes too long time!

I am trying to solve the following problem numerically and I faced two things: 1- It takes too long time to give solutions. 2- there are many roots for the equation but NSolve doesn't give all thee ...
3
votes
1answer
94 views

How to efficiently find only the rational roots of a rational complex polynomial?

I need to find all the rational roots of a bunch of high-order polynomials with rational complex coefficients. Is there an efficient way to do this? My best effort on an example polynomial: ...
0
votes
1answer
38 views

Why do I not get a result when there is no error message? [closed]

I've typed in the following equation: Solve[((h*s + l - r*s - r)/(s^2 + s)) (1 + s) - h == (h*s + l - r*s - r)/(s^2 + s) - r, r] and it produces: ...
3
votes
1answer
57 views

How can I choose the coeffcients so that the givent system of equations has four integer solutions?

Consider the system of equations with unknown are $(x,y)$. $$\begin{cases} a_1x^2+b_1y^2 + c_1xy+d_1x + e_1y+f_1=0,\\ a_2x^2+b_2y^2 + c_2xy+d_2x + e_2y+f_2=0. \end{cases}$$ I want to find the ...
2
votes
0answers
112 views

Why can't Mathematica solve this equation? [duplicate]

Possible Duplicate: Can Reduce *really* not solve for x here? Why can't Mathematica solve this equation? ...
4
votes
1answer
110 views

Does Solve[] find ALL the exact roots of rational polynomials?

Does Solve[] find ALL the exact roots of rational polynomials? I've done a bunch of tests where I created an expression with some analytic roots, and Solve[] always found them all. But is the ...
12
votes
2answers
2k views

Error entering equation in DSolve

I entered a command incorrectly as follows: DSolve[{y'[x]=y[x]},y[x],x] I am now experiencing: ...
1
vote
1answer
155 views

How do you solve a linear equation of matrices? [duplicate]

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
vote
3answers
254 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 ...