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

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2
votes
1answer
307 views

Solving System of Inequalities Relatively

I have been trying to figure out how to solve a system of inequalities relatively. I don't care about values, I just want all possible ordering. An example system might be:$${b > r,\; p > r,\; c ...
0
votes
1answer
311 views

NDSolve + FindRoot for Bessel Zeros

I am trying to use a solution given by Michael E2 in this topic: ...
1
vote
2answers
157 views

Symbolic matrix equation

I am looking to a system of equations of the form $\pi =\pi P$, the one encountered in Markov chain theory. My $P$ variable is: ...
3
votes
2answers
603 views

How to solve a “tensor equation”?

I am trying to solve equations which looks like this: $$ T_{ab} - T_{bc} = a_1 T_{ab} + a_2 T_{ac} + a_3 T_{bc}, $$ where $T_{xy}$ are tensors. I want to get the $a_i$'s (in this simple example ...
1
vote
1answer
107 views

How do I get Nsolve to work with hyperbolic functions?

This is a rather simple numerical solution, but it simply doesn't work. Does anybody have a solution? NSolve[x - Sinh[x] - 1 == 0, x] NSolve::nsmet: This ...
-1
votes
3answers
2k views

How do I determine the maximum value for a polynomial, given a range of x values?

I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
1
vote
1answer
271 views

General form of a linear transformation

Let $v_1 = \begin{bmatrix} 2 \\ -1 \end{bmatrix}$ and $v_2=\begin{bmatrix} 1 \\ -1 \end{bmatrix}$ and let $A= \begin{bmatrix} 3 & 2 \\ -2 & 1 \end{bmatrix}$ be a matrix for $T\colon \Bbb ...
1
vote
1answer
502 views

Solving a nonlinear system of recurrence equations

I am having two problems regarding Mathematica, and both of them are happening because it does not accept such inputs: ...
1
vote
1answer
77 views

Find the point that holds a given property

I have a normal distribution with mean 106, and a standard deviation of 8. I'm being asked to find the point that has the property that 25% of these values have this value or lower. What I've ...
0
votes
1answer
224 views

Solve Probability of Distribution

Why does this work: Solve[Probability[x <= t, x \[Distributed] NormalDistribution[]] == 0.95 ,t] But this doesn't: ...
2
votes
1answer
415 views

FindRoot giving false roots with Bessel Functions

I have read in some places about the errors associated with FindRoot, but the closest thing I can find on this website seems to be due to the imaginary unit. I am dealing with what should be a ...
7
votes
2answers
276 views

Using NSolve in the complex plane

I am trying to find numerical values for $\Im\ e^{\frac{1}{2} +i\ y} = \Im\ \zeta(\frac{1}{2} +i\ y)$ for a given range. I have tried: ...
14
votes
3answers
2k views

How can I implement the method of Lagrange multipliers to find constrained extrema?

I want to form the function $h=f-\lambda_{1}g_{1}-\lambda_{2}g_{2}$ where $f$ is the function to optimize subject to the constraints $g_{1}=0$ and $g_{2}=0$ so that I can solve the first partial ...
-1
votes
1answer
232 views

Efficient Table Generation & NDSolve Error

I'm currently working on solving an SEIR model with data from the CDC. I've created a function to calculate the Square difference for the model and want to create a table of values for the 4 variable ...
1
vote
0answers
280 views

Solving asymptotic equations

Let's say I have several equations that have solutions given as a negative series $$y(t,x)=\sum_{n=-1}^\infty a_n(t) x^{-n}=a_{-1}x+a_0+a_1x^{-1}+\mathcal{O}(x^{-2})$$ My equations look like ...
1
vote
0answers
80 views

Simple Solve example fails: why? [duplicate]

Solve is an amazing tool, but sometimes it doesn't work in the way I expect it to. The particular instance that is confusing me right now is this: ...
0
votes
1answer
176 views

Plotting a function only non-zero for discrete values of argument

I have a function like: $$ f(E)= \Sigma_{n=0} \Sigma_{\ell=0} \, \delta\left(E+\frac{\ell+2n+2} {R\sec{\rho}}\right) w(n,\rho,\ell)\,, $$ i.e. the function is zero unless $$ ...
1
vote
1answer
252 views

Gram Schmidt inner and outer products

I know the Gram-Schmidt orthogonalization generates an orthonormal basis from an arbitrary basis. I need help with: Write a program that inputs a list $\{b_1,\dotsc,b_n\}$ of linearly independent ...
4
votes
1answer
217 views

Numerical errors/inaccuracies in ProductLog

Context In cosmology, a fairly accurate model to describe the gravitational potential, $\psi(r)$ of dark matter halos is given by $\psi( r)=\log(1+r)/r$. ...
1
vote
1answer
101 views

Solve failing and not clear why

I define the function: w[q_, n_, a_] := q/(4 Pi n r^2) (1 - Exp[-2 r/a] (2 (r/a)^2 + 2 (r/a) + 1)) I then want to solve: ...
5
votes
2answers
389 views

Intersection of two splines

I have a collection of sets of points, each set defining the segment of a (nice) curve on the unit sphere $S^2 \subset \mathbb{R}^3$. The points are computed numerically. I now want to compute the ...
2
votes
2answers
163 views

Incorrect numerical derivative of function that uses FindRoot

I am trying to plot the derivative of function g[x] below where g[x] is defined as the root of another equation. However, I am ...
0
votes
1answer
72 views

Issues FindRootPlot command

I've had some fun playing around with FindRootPlot for a simple system of equations: ...
2
votes
0answers
118 views

Question about Solve

I don't understand what Mathematica is doing to get these solutions. I ask it to solve two equations, the left hand side of both expressions are the same, the right hand sides differ by a ± sign. I ...
7
votes
1answer
422 views

Issue with the NDSolve code

With this procedure, one may determine an eigen-value function $R(a)$ for any given $\Xi$ (say 0, 25, 50, 75, 100) ...
4
votes
2answers
119 views

Non-convergance of the solution of the 1+1 partial differential equation

I am stacked with a partial differential equation as follows: This is the $\LaTeX$ expression for the equation $$ \frac{\partial y}{\partial t}=\frac{\partial^2 y(x,t)}{\partial x^2} ...
3
votes
3answers
142 views

Find $Y \in (0, 5)$ such that the roots of $4x^2 + 4xY + Y + 2 = 0$ are real?

The problem is to find all $Y \in (0, 5)$ such that the roots of $4x^2 + 4xY + Y + 2 = 0$ are real. I took a straightforward approach with Mathematica with the intent of listing the only solutions ...
0
votes
1answer
744 views

DSolve to solve a system of differential equations [duplicate]

I need to solve a system of differential equations as follows: ...
5
votes
0answers
82 views

Using quantifiers with free indices as declarative conditions in equation solving

This is a toy example: Is there a way to rewrite ...
6
votes
1answer
169 views

The third argument of the Root function

Consider the roots of an arbitrary indecomposable polynomial: sol = Solve[x^5 + 2 x + 1 == 0, x] The returned expression is ...
1
vote
1answer
198 views

Solving an exponential multivariate equation

I have the following equation: p = 1/(1 + E^(-51.179 + 0.849 x1 + 2.3649 x2 + 1.155 x3 + 1.46 x4 + 1.31 x5)) and I want to find the set of values for x1 to x5 ...
0
votes
1answer
166 views

How to return the rhs of a transformation rule from within Compile[]

I have defined the following function: ...
0
votes
1answer
233 views

Solve[polynomial, x, Reals] doesn't get all real roots or correct ones?

My main confusion is about the difference between the two code blocks at the end of this long spiel, but the spiel contains the code to create the polynomial if its coefficients are helpful for ...
0
votes
1answer
131 views

Manipulating and using result of DSolve

I have an unsightly looking equation that nonetheless has an analytical solution. The solution is ugly as hell, but exists; I use the following code with the DSolve ...
3
votes
1answer
203 views

When does the real part of Zeta vanish on the critical line?

This seems to be a quite a simple problem but I cannot make it work. I am trying to find all values within a given range for which the real part of the Zeta function vanishes on the line: ...
1
vote
3answers
150 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
1answer
949 views

Singularity / stiffness / precision errors with NDSolve

I have a relatively simple 2nd Order ODE problem I'm trying to solve numerically $p'' + \frac{1}{r}p' = A(\frac{p(r)}{p(r) + k_{m}})$ where $A = 7.5795*10^9$ and $k_{m} = 1$. So trying to get ...
1
vote
0answers
40 views

How can I access numerical values of variables calculated with Solve? [duplicate]

I am trying to calculate some thermodynamical cycles so I often use lists with equations. Here's a simple example: ...
1
vote
2answers
196 views

Setting up and solving system of equations

Consider the following code: ...
1
vote
2answers
159 views

ReplaceAll a list of rules to an equation

Given the following equation and rule, how would I Solve the equation for tr, k and ...
0
votes
1answer
416 views

Solve the quadratic equation? [closed]

I can't seem to solve the general quadratic equation: Solve[ax^2 + bx + c == 0, x] Out[299]= {} It just outputs the empty list. How do I solve this equation?
0
votes
2answers
95 views

Gaps in plots of equation solution from parameter

I'm trying to plot solution of system of equations as a function of parameter ...
1
vote
1answer
113 views

Passing f[x][[1]] to FindRoot [duplicate]

FindRoot seems to fail for most examples of the form f[x_?NumericQ] := {x - 3 , x^3}; FindRoot[f[x][[1]], {x, 3}] ...
0
votes
0answers
87 views

DSolve is rejecting my description of a system of PDEs

I am trying to solve a system of partial differential equations using DSlove. But i get the input equations in return. Dsolve is not doing anything ...
1
vote
3answers
394 views

Can plot a function, NSolve takes too long

I'm new to Mathematica, so maybe mine is an easy to solve issue, but I haven't been able to figure it out. I have a series of linear ODEs I solve using for: ...
-2
votes
1answer
156 views

Proof: Convergence of an equation and show the first derivative is bounded

We have the following equation \begin{equation} x(k+1)=\arccos\bigg( -\frac{1}{2(Dr^{\frac {|\sin(2x(k)+\theta)|}{M\sin x(k)\sqrt{A+2B\cos(2x(k)+\theta)}}}+1)} \bigg) \nonumber \end{equation} ...
1
vote
1answer
192 views

Defining a curved region for NDSolve

I have an equation to solve using NDSolve which involves two parameters: $en$ and $k$. The equation produces a set of curves when $en$ is plotted against $k$. In ...
1
vote
1answer
250 views

Plot the solution complex transcendental equation

I'm trying to plot an implicit function satisfying a complex transcendental equation. The code is the following: ...
3
votes
3answers
198 views

What is the formula for this numerical series?

I'm developing a questions game. My goal is that the score for each correct answer will increase as the user answers more questions. Initially there are 15 points for each correct answer. Every 4 ...