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

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3
votes
3answers
346 views

How can I calculate a combination of limit and sum?

How can I solve the above problem? I enter it as: Limit[Sum[Sqrt[1 + i^2/n^2]/n, {i, n}], n -> Infinity] but this is not working:
1
vote
1answer
186 views

NSolve with numerical function

I would like to solve numerically an equation which involves a numerical function constructed by fitting some data: ...
0
votes
3answers
342 views

Solving a differential equation with mixed conditions using DSolve

I want to solve a differential equation $$ \frac{d}{dx}\left(k_0 \left(\frac{T(x)}{T_0}\right)^n \frac{dT(x)}{dx}\right)=0,$$ with boundary conditions: $T(l)=T_0$, $\;T'(0)=-\frac{q_0}{k_0 ...
2
votes
2answers
239 views

Check if integer has even number of digits

I want to check if a number has an even or odd number of digits. 10 would be even because it has 2 digits 300 would be odd ...
10
votes
3answers
404 views

Reduce can't reduce an equation without appropriate assumptions

When there are three unknowns (x, y, z), Mathematica can solve it: ...
4
votes
5answers
475 views

Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
2
votes
1answer
165 views

How can I exhibit the evaluation of formulas in a Mathcad-like way?

How can I create a function F that works like this: x = 2 f1 = x^2 + 3 f2=x+5 F[f1] x^2 + 3 = 2^2 + 3 = 7 ...
0
votes
1answer
614 views
1
vote
0answers
325 views

Differential equations: How do I solve a delay differential equation with 0-1 variables

How do I solve the following non-linear, delay-differential equations using Mathematica under the assumptions $$p(t) = 1 ,\; y(t) > k$$ $$p(t) = 0,\; y(t)<= \ k$$. $$ \frac{dw}{dt} = ...
9
votes
1answer
909 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 ...
1
vote
0answers
384 views

Why DSolve and NDSolve give different answer

Consider these code, which solve the same equation using DSolve and NDSolve, why do they give different answer? Which one is ...
0
votes
1answer
142 views

Small problem at equation solving

I have $2$ equations in $2$ parameters which involve integrations. The limits of the integrals can not be defined analytically. They also require equation solving and eventually I couldnt incorporate ...
2
votes
1answer
113 views

Plotting the solution of a 2nd order equation

I have got to solve a second order equation, where the coefficient depend on the parameter $k$: $$(A_k - \omega) (D_k- \omega) - B_kC_k = 0$$ so that also the solution $\omega=\omega(k)$ will depend ...
2
votes
1answer
318 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
326 views

NDSolve + FindRoot for Bessel Zeros

I am trying to use a solution given by Michael E2 in this topic: ...
1
vote
2answers
161 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
618 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
110 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
282 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
514 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
79 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
229 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
439 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
282 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
240 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
288 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
183 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
269 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
220 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
102 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
395 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
167 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
74 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
427 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
143 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
868 views

DSolve to solve a system of differential equations [duplicate]

I need to solve a system of differential equations as follows: ...
5
votes
0answers
84 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
172 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
214 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
171 views

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

I have defined the following function: ...
0
votes
1answer
245 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
134 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
204 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
151 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) ...