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

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0
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1answer
84 views

Many NSolves to interpolating function

I have an expression of the form: expr = TerribleNumericalFunction[U[p]] == SimpleFunction[p] The Simple function is a ...
0
votes
1answer
104 views

NDSolve issue with initial and boundary conditions

While solving the heat equation in one spatial variable $u_t = u_{xx} $ (x goes from 0 to L) with the initial temperature distribution $T_0 \frac{x(L-x)}{L^2}$ , and with neumann boundary conditions ...
2
votes
1answer
62 views

How to solve an equation given certain parameters?

I am new to Mathematica so please bear with me. I have an equation that has around 7 parameters and one unknown. I was able to use FindRoot to solve it; however, I ...
4
votes
2answers
82 views

Plotting results from Findroot

I know this has been asked, but I cannot seem to understand the solutions. What I need to know, because I have my first domiciliary test this Monday, is how to plot the output from ...
6
votes
2answers
129 views

NSolve erroneously gives no solution to a polynomial system

I have a polynomial system with three equations in three unknowns, the maximum degree is 26. Two equations are symmetric, i.e. eq1(x,y,z)=eq2(y,x,z). If I search ...
0
votes
1answer
70 views

Find all degenerate eigenvalues of a cubic equation

I have an equation that is cubic in w. The three solutions correspond to bands in a bandstructure, and are a function of wavevector ...
5
votes
3answers
186 views

Finding the conditions for degenerate solutions to a cubic equation

I have a cubic equation (corresponding to the band structure of a physical system) given by w in the code below. ...
0
votes
1answer
64 views

NSolve or Reduce for obtaining the results and connecting roots

Here I have one problem how to solve numerically equation for different values of one parameter x. I used just two digits because of length, but for x=0.57 I should have one real root and for others ...
5
votes
2answers
156 views

Solve for x given an interpolation function, y

Given a list of data, lst={{x1,y2},{x2,y2},...,{xn,yn}} and the interpolation function fun, y=Interpolation[lst] which ...
1
vote
1answer
84 views

solving system of non-homogeneous advection equation using mathematica?

This question is followed up from this question How to solve a certain coupled first order PDE system Here I consider the non-homogeneous advection system \begin{equation} ...
1
vote
1answer
94 views

How to solve a certain coupled first order PDE system

I would like to find the solution $(U,V)\equiv (U(x,t),V(x,t))$ of the following system. \begin{equation} \displaystyle\left\{\begin{array}{l} \frac{\partial U}{\partial t}+(a+b x)\frac{\partial ...
5
votes
2answers
259 views
15
votes
2answers
1k views

How do I split up a curve into chords of equal length?

I have a curve that is defined as f[x] and what I'm attempting to do is to divide the curve into equal straight lengths for a number of segments of my choosing that I've defined as nSeg. I've created ...
5
votes
2answers
459 views

Finding Points of Tangency of a Circle and a Parametric Curve

I have the following Parametric plot Generated from the following: ...
1
vote
1answer
81 views

cross point of intersecting lines [duplicate]

What is the easiest way to find the crossing point of two intersecting lines passing lets say through points line1 = {p1,p2}, line2 = {p3,p4}?
5
votes
0answers
95 views

Using quantifiers with free indices as declarative conditions in equation solving

This is a toy example: Is there a way to rewrite Reduce[{Norm@{c[1], c[2], c[3]} == 1, 0 <= c[1] < c[2] < c[3]}, {c[1], c[2], c[3]}] ...
0
votes
0answers
24 views

Find Multi-variable intervals with given constraints in complicated expressions

I am working on finding variables' intervals that satisfy some conditions and subject to some relations. At first, these variables have intervals pre-defined as follows: $$0 < \alpha, \beta, ...
2
votes
3answers
156 views

Solve a transcendental equation in Mathemathica

I believe it is called a "transcendental equation", and I would like to find the best possible sollution. I tried to use Solve: ...
3
votes
1answer
153 views

Finding closest point to implicitly defined curve

I'm facing the following problem: Given an implicit curve given by $f(x,y)=0$ and an initial guess $(x_0,y_0)$ which is hopefully close to the curve, I want to find the point $(x,y)$ on the curve ...
2
votes
1answer
405 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 ...
-1
votes
0answers
8 views

Create formula to get a value [migrated]

I have clients whichs pay a monthly fee. I would like to know the accumulative total for a given quantity of month for a given fee. Plus I get 2 new clients every month. Let's say a client pays ...
22
votes
2answers
1k views

Using the Krylov method for Solve: Speeding up a SparseArray calculation

I'm trying to implement this Total Variation Regularized Numerical Differentiation (TVDiff) code in MMA (which I found through this SO answer): essentially I want to differentiate noisy data. The full ...
3
votes
1answer
197 views

Faster Solve for Fermat 4n+1 conjecture

Assuming that Fermat 4n+1 conjecture (each prime of the form 4n+1 is the sum of two squares) is true then I like to solve the ...
1
vote
1answer
68 views

Solving a transcendental equation

I want to solve the a transcendental equation, e.g. NSolve[-(1-x)*Log[1-x] - x*Log[x] == 0.5, x] Mathematica is not able to solve, wheres WolframAlpha -- is able ...
1
vote
1answer
65 views

Reduce Inequality

How can I reduce the inequality in terms of modulus of alpha. ...
2
votes
1answer
83 views

Implicit derivatives in one line. How do I do it?

I have this little script to derive implicitly $PrePrint = # /. {D[y_, x_, NonConstants -> {y_}] :> y'[x]} &; Example: ...
1
vote
0answers
56 views

How to solve a nonlinear overdetermined system of equations

i'm trying to solve a nonlinear overdetermined system of equations (124 equations, 123 variables) i tried this procedure (newton raphson) ...
2
votes
2answers
223 views

Finding integral points on a surface

Suppose I have a dimension formula (for a Lie algebra representation) that is as follows: $$ d(a,b) = {(a+1)(b+1)(a+b+2) \over 2} $$ Now consider the surface $F(a,b,n) = 0 = d(a,b) -n$ where $n \in ...
3
votes
1answer
547 views

Methods for NSolve

I've been using NSolve a moderate (50-100 equations) size system of linear equations and it has been working splendidly (Solve ...
20
votes
6answers
3k views

Finding the intersection of a curve with an interpolation function

There are no issues trying to find the intersection points of two defined curves. ...
7
votes
3answers
325 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: ...
0
votes
2answers
85 views

Significantly different results between Mathematica and Wolfram Alpha with large radicals and small numbers [closed]

I have some code which involves tiny numbers being put to the power of very large numbers. The function I'm looking at is $\varphi = \omega(T) \left(1 - (1 - \epsilon)^{n_{e}(T)} \right)$ when ...
2
votes
2answers
144 views

Solving a system of weird equations

I'm trying to have Mathematica solve a system of equations for a friend's work in Computer Vision. I'm essentially going in blind to this and am not very familiar with Mathematica syntax, so would ...
2
votes
1answer
81 views

Can't NSolve system of exponential and linear equations in several variables

At the moment I am stuck with the following code, when specified to use root , quadratic or log utility functions all it fine, only exponentials like: $\small \left\{-e^{-c_{0,1}}-0.25 ...
4
votes
1answer
240 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 $\psi( r)=\log(1+r)/r$. ...
0
votes
1answer
61 views

Removing imaginary and negative results from Solve

I have been trying to solve a series of equations that I know have real positive values for the unknowns (they all have real world analogues and they are not linked to a frequency domain) but despite ...
15
votes
5answers
770 views

How to make a Line[] with no end?

I'm trying to do this: In this graph, the secant points are aproximated in order to become the tangent, it seems I need some kind of function which plots a line based on two points and it's points ...
1
vote
0answers
37 views

DSolve -> no results

I am trying to solve a system of differential equations. ...
0
votes
2answers
56 views

NSolve not solving [closed]

I've been working on a Newton Cooling equation problem for my diff equ class and cannot get NSolve to solve this equation. I've plugged it into Wolfram Alpha and my ...
0
votes
0answers
177 views
14
votes
3answers
396 views

Solve a trig equation system

Background of the problem In the same plane, P is a fixed point, A,B,C are moving point, PA=a, PB=b, PC=c, find the maximize perimeter of △ABC. let ∠BPC=A, ∠CPA=B, ∠APB=2*Pi-A-B, then the ...
0
votes
1answer
73 views

Elements inside arrays seem to be strings rather than signed numbers

When I have code like b = Array[Subscript[be, #] &, {3, 1}] b = b /. {Subscript[be, k_] :> Subscript[-be, k] /; k > 1} I am noticing that Mathematica ...
5
votes
2answers
246 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 ...
4
votes
1answer
375 views

3D Plot of The Riemann Zeta Function

I am a new user and i would appreciate your help to visualize the 3D of the following function. Edit I tried this ...
2
votes
2answers
136 views

Solving for any one variable in a formula given values for all the others

Suppose I have an equation relating a number of variables and I know the values of all but one of them. Using the equation and known values as input, is there a simple command (built-in or otherwise) ...
0
votes
1answer
360 views

How to use `FindRoot` to solve an equation containing a parameter?

I'm trying to derive some of the results of the following paper: Electrodynamics of semiconductor-coated noble metal nanoshells, JT Manassah - Physical Review A In the paper there is matrix $\mathbf ...