Questions tagged [equation-solving]

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

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Reduce[Sin[x]==0,x] splitting odd and even multiples of Pi

as from Title, I'm wondering why Mathematica does not automatically give a single, simple solution for the problem Reduce[Sin[x] == 0, x] for which I obtain the ...
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7 votes
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246 views

Spurious DSolve Solution

Bug introduced in 8.0.4 or earlier, persisting through 12.0. DSolve quickly returns solutions to the following PDE (which is the homogeneous portion of the PDE in ...
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Does NSolve find all solutions?

Is the solution set returned by NSolve usually complete? Can I assume that there are no more solutions than what it returns? Consider systems of equations e.g. ...
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Strange behaviour of NotElement in Reduce

Bug introduced in 8.0 or earlier and fixed in 11.0.0. Confirmed, as bug, by WRI: [CASE:3527549] I have observed curious behaviour on domains supplied to NotElement...
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7 votes
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Solve huge symbolic system of linear equations

I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[] nor ...
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6 votes
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Limitations in using Reduce for Integer systems

The System For example, when solving the following system using Reduce in Integers: ...
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94 views

When does Root have a third argument

In Mathematica "11.0.1 for Microsoft Windows (64-bit) (September 20, 2016)", Root[#^4 + 1 &, 2]; actually has three arguments, as can be seen from ...
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6 votes
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367 views

Solving a nasty equation

Here's an equation that I need to solve for $t_k$ $$ \theta_0 = \tan^{-1}\left(\frac{2(w_x - m)}{p - g {t_k}^2 - 2 t_k w_y}\right) - {\frac{1} {r}} \left( \left(\frac{m}{t_k}\right)^2 + \left( \frac{...
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5 votes
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Making Intersection of 3 Lines Calculation More Efficient

So I managed to optimize the calculation a little for looking for 3 line intersections in equally spaced points around a circle by only checking one "wedge" of the circle, ignoring ...
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5 votes
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How to get an asymptotic of the real-valued branch of the inverse function?

Consider function $f:\mathbb R^+\to\mathbb R^+$, defined as $f(x) = x + x^2\left(1 + \log x\right)$. I need to find an asymptotic approximation of its inverse function $f^{\small(-1)}\!:\mathbb R^+\to\...
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5 votes
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200 views

Incorrect result by DSolve

For real $x$ consider the trivial equation $$|y'(x)|=-|x|.$$ Since the left side is always positive and the right always negative, there is no solution. Let's try ...
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Finding periodic cycles of a function

Given a function f[{x,y}] it is rather simple to use, for example, NSolve to find periodic points of period $n$. We simply take ...
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How does NSolve find the roots to an equation?

I'm using NSolve to find the roots to a transcendental equation. For this, I need to specify a bounded region where roots are searched. What I want to know is how <...
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5 votes
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955 views

Solving a system of differential algebraic equations (DAE)

I am trying to solve a system of 8 differential algebraic equations, where equations 3 and 5 are differential equations and the rest are constraints which need to be satisfied. Also I only know the ...
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Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
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5 votes
0 answers
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How to find an algebraic representation

I want to find matrix representation of some algebra (Clifford algebra Cl(3,1) in this case). Here is an example, which I would like to get and then extend to higher dimensional matrices. Suppose we ...
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Method of characteristics, recursion formulas

I'm helping a friend out with a problem. He needs to plot out the solution to a water surge in a pipeline. I have all the parameters set and I've put the equations in Mathematica, but I can't get the ...
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Reduce doesn't solve this equations with condition

Reduce[{4==Abs[-1+2 Cos[2A]+2 Cos[2B]+2 Cos[2(A+B)]]},{A,B},Reals] worked well, but ...
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Suggestions for solving a large linear system

I have a system of $\approx 200,000$ linear equations in $\approx 40,000$ variables (with rational coefficients) and I would like to determine the dimension of the solution space, which I know to be ...
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5 votes
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114 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]}] ...
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4 votes
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130 views

Constructing a Lyapunov function for this system?

This question seems interesting but I cant figure out how to apply Micahel E2's solution to my system: How to write that Lyapunov function? My system is very simple, I already have a working Lyapunov ...
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4 votes
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Finding Coefficients in a Perturbation Problem related to Chaotic Dynamics

I am trying to reproduce the results from this paper: Chaotic dynamics of a suspended string in a gravitational background with magnetic field I am currently stuck with finding the coefficients. First ...
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Force Solve to respect unit system

I give Solve quantities in FPS and it returns resulting quantities in SI, necessitating that I add an entire section to my workflow where I pick apart the solution ...
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4 votes
0 answers
128 views

Indicate Unit Vectors in Solve

I'm solving a system defined by two rays. The rays originate from two points {x,y,z} and {x,y,z-h}. They go in directions (unit ...
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4 votes
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149 views

DSolve, NDSolve with WhenEvent Give Incorrect Solution for Simple ODE

NDSolve Results On the course of addressing question 181974, I encountered the following problem. ...
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4 votes
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181 views

Discordance in plots

Let us solve the system with Floors ...
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4 votes
0 answers
58 views

A simple expression on which `Reduce` fails

The conditions in x ∉ Integers && y ∈ Integers && y == -(1/2) + x/2 are inconsistent but Reduce does not solve ...
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4 votes
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248 views

Why does Reduce[x + 1/x == 1/x, x] give the result x == 0, instead of the result False?

Why does Reduce[x + 1/x == 1/x, x] give the result x == 0 instead of the result False? There is no value of x that causes ...
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4 votes
0 answers
112 views

Order of evaluation of FunctionDomain, Reduce, Solve, etc

For the input (mine is much more complicated, this is a toy example): x/x /. x -> 0 the output of 1 (as opposed to ...
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4 votes
0 answers
477 views

Homotopy Continuation solution of system of polynomials

I have very large systems (>20) of polynomial (max degree 3) equations that I would like to find a solution to. I'm not interested in all solutions as presumably there are too many (a huge number ...
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4 votes
0 answers
121 views

Why does Solve work in v9.0.1 but not in v10.3.1

I want to solve the following DE $$ P'=k(M-P)P, P[0]=53.08, P[50]=23.192, P[100]=76.212.$$ The Mathematica command is ...
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4 votes
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381 views

Complex boundary conditions and NDEigensystem

I am having difficulties implementing a Neumann value when numerically solving the Navier equation using NDEigensystem. The Navier equation is given by $\nabla^2 \vec u + (p^2 - 1) \nabla(\nabla\...
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440 views

Extending Bresenham's algorithm for subpixel rendering

Original Bresenham's line drawing algorithm it limited to drawing lines between two integer pixel positions and does not allow subpixel rendering. However with my reformulation of this algorithm as a ...
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4 votes
0 answers
355 views

Stability analysis of transcendental equation (stability crossing curves)

I am working with a non-linear delay system with three scalar delays. After taking the Laplace transform of the linearized system, the characteristic function is a transcendental equation with three ...
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4 votes
0 answers
301 views

Solving Thue equations

A Thue equation is a 2-variable homogeneous integer polynomial of degree at least 3. It's well-known that such equations have only finitely many solutions over the integers. I'm trying to solve some ...
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4 votes
0 answers
416 views

Am I entering this 2-variable recurrence correctly?

I'm trying to solve this recurrence with two variables. RSolve[g[d, n] == 1 + g[d - 1, n] + g[d - 1, n - 1] && g[d, 0] == g[0, n] == 0, g[d, n], {d, n}] ...
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  • 555
4 votes
0 answers
172 views

Symbolic solution to ODE, pure InverseFunction not evaluated

I'm new to Mathematica and I don't understand why in the solution of the following ODE, the #1 in the pure function is not immediately replaced by the corresponding ...
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  • 339
3 votes
0 answers
89 views

Solving or Minimizing the Norm of the matrix equation $M^TAM - M^TB - B^TM =C$

I am trying to solve the matrix equation $M^TAM - M^TB - B^TM=C$ where I know A, B and C. My unknown matrix is M which has the special form that all the rows and columns sum to zero. i.e. I have four ...
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  • 485
3 votes
0 answers
34 views

Numerically solve a non-differential equation with InterpolatingFunction as output

I have some a function that I need to solve numerically over an entire domain (Ideally I would like an InterpolatingFunction object as output), which does not include any derivatives. I have found a ...
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3 votes
0 answers
75 views

How to improve this code?

The aim of my work is to find a value for the complex constant $\omega$. In order to do that I solve the below system of differential equations with a manual shooting method: I first solve the system ...
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3 votes
0 answers
62 views

Different output to Solve command in Mathematica changing a variable for a subscripted variable

I have a system of equations that is solved with the Solve command in Mathematica 10.2, when one of the variables is changed for a subscripted variable the answer is not the same, the difference is ...
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3 votes
0 answers
203 views

Errors Using FindFit and FindRoot

I'm trying to fit the following equation to data: where and x and y are the dimensionless variables x=V/Vr and y=Ir/(2*I0). n=1 and I'm trying to find Vr and R. The blue is an example of the curve ...
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3 votes
0 answers
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Unexpected Behavior of Parametric Sensitivity in ParametricNDSolveValue

Bug introduced in 10.4 or earlier and continuing through 11.3 Submitted as CASE:3916971 While exploring alternative methods of solving 33538, I encountered difficulties with the parametric ...
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3 votes
0 answers
136 views

Solving Monster Equations with Mathematica

I would like to solve the following equations in Mathematica. Here are the formulas: $u=0.5$ $\alpha=0.5$ $\epsilon_0=0.1$ $\epsilon_1=0.1$ $f_0(y)=\mbox{Gaussian density with mean -1 and ...
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3 votes
0 answers
170 views

Replace all (/.) parameters with equation or condition rather than single values

Suppose that one wants to calculate the surface charge density of a polarized dielectric ellipsoid, prolate ellipsoid with long and short axes as $a$ and $c$ where $a$ is parallel to the $z$ axis. $a$ ...
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  • 249
3 votes
0 answers
534 views

Solve PDE over time-dependent region

I have some experience with C++ programming, but I am quite new to Mathematica and I think the latter requires a different mindset which I am still not used to. I would like to simulate the effect ...
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3 votes
0 answers
100 views

Does Reduce have problems with greek symbols that lead to wrong results?

I call Reduce on the following simple system of inequalities ...
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  • 31
3 votes
0 answers
106 views

Spheroidal Eigenfrequency

I am trying to create a Mathematica function which will calculate the eigenfequencies of a spheroidal cavity. The expressions I use are based both on the book "Spheroidal Wave functions in ...
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3 votes
0 answers
84 views

Generating All Regular Multigraphs -- Issue with Solve and/or FindInstance

I'm looking to generate all regular multi-graphs over $n$ vertexes and of degree $d$ in mathematica (side note: $n,d$ are fairly small, this problem gets unmanagable very fast). So here $n,d$ are my ...
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3 votes
0 answers
157 views

Problem solving optimal stopping PDE

I am trying to solve a PDE that is coming up in a control problem. So far I have the following: ...
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