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

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10
votes
3answers
395 views

Reduce can't reduce an equation without appropriate assumptions

When there are three unknowns (x, y, z), Mathematica can solve it: ...
3
votes
3answers
338 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:
0
votes
0answers
129 views

Assigning the answer of Solve to a variable [duplicate]

If I enter Solve[(x-2)(x+2)==0,x] then the answer comes up as {{x -> 2}, {x -> -2}} I want to make two variables ...
0
votes
3answers
338 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 ...
4
votes
5answers
463 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 ...
1
vote
1answer
146 views

Solve returns a wrong answer

I'm afraid the following is rather localized questions, but I don't know how to simplify and generalize it. I have the following two points (in the real plane): ...
1
vote
1answer
182 views

NSolve with numerical function

I would like to solve numerically an equation which involves a numerical function constructed by fitting some data: ...
2
votes
2answers
232 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 ...
1
vote
0answers
315 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} = ...
10
votes
1answer
420 views

Mathematica implementation of Earth Movers Distance?

Has anyone implemented in Mathematica the Earth Mover's Distance (EMD)? A concept dating back to Monge 1871, used to compare histograms and images, e.g., the CIEDE2000 Color Difference algorithm. ...
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
316 views

NDSolve + FindRoot for Bessel Zeros

I am trying to use a solution given by Michael E2 in this topic: ...
7
votes
1answer
857 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
361 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 ...
3
votes
2answers
606 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 ...
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
310 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 ...
7
votes
1answer
423 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) ...
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: ...
1
vote
1answer
503 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
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
78 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 ...
2
votes
1answer
423 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 ...
5
votes
1answer
2k views

Solving a system of linear equations modulo n

I have a system of linear equations $$ a+b+c \equiv 31 \pmod{54} $$ $$ 4a+2b+c \equiv 3 \pmod{54} $$ $$ 9a+3b+c \equiv 11 \pmod{54} $$ What should I input (I'm using ...
6
votes
1answer
537 views

Issue with NSolve

I defined the following function: sw[ θ_, ϕ_, h_] = 1/2 Sin[2 (ϕ - θ)] + h Sin[ϕ] Based upon whether I use Solve or NSolve, ...
2
votes
3answers
263 views

Minimization problem

How could you find the smallest constant $c$ that satisfies $$\frac{3^{3k}e\sqrt{3}}{\pi\sqrt{k}\;2^{3/2+2k}} \leq 2^{\;c\;k}$$ assuming $k\geq 1$ is an integer. You can of course take logs of ...
-1
votes
1answer
234 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
178 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
262 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 $\psi( r)=\log(1+r)/r$. ...
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 ...
5
votes
2answers
391 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 ...
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: ...
2
votes
2answers
164 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 ...
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} ...
0
votes
1answer
73 views

Issues FindRootPlot command

I've had some fun playing around with FindRootPlot for a simple system of equations: ...
0
votes
1answer
773 views
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 ...
5
votes
0answers
83 views
1
vote
1answer
204 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
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) ...