Questions tagged [equation-solving]

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

511 questions with no upvoted or accepted answers
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7
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0answers
719 views

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. ...
7
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252 views

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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89 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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175 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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2k views

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 ...
6
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0answers
331 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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49 views

Limitations in using Reduce for Integer systems

The System For example, when solving the following system using Reduce in Integers: ...
5
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274 views

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 <...
5
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187 views

General solution of inscribed square problem

There is my earlier question about Inscribed square problem Now I tried to find the general solution for any curve $f(x,y)=0$. For instance : $\qquad \left(x^2+y^2-1\right)^3-x^2 y^3=0$ ...
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646 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 ...
5
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159 views

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 ...
5
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284 views

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 ...
5
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247 views

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 ...
5
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120 views

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 ...
5
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472 views

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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466 views

What is the algorithm used by Reduce for this equation?

Mathematica can use Reduce to arrive at an answer in the following equation: ...
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110 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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114 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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165 views

Discordance in plots

Let us solve the system with Floors ...
4
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0answers
49 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 ...
4
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167 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 ...
4
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0answers
107 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 ...
4
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104 views

How to extend a root finding method from 1D to multi dimensions

The number (0.25 Pi) is a third order root of f[x] below. Clear[f]; f[x_] := Sin[x] - Cos[x] - Sqrt[2] (x - 0.25 Pi); Chop@Normal@Series[f[x], {x, 0.25 Pi, 4}] -...
4
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0answers
342 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 ...
4
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120 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 ...
4
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336 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\...
4
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328 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 ...
4
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244 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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406 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}] ...
4
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152 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 ...
3
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0answers
57 views

Why does FindInstance take so long: It is faster with more restrictions than with less?

A support case with the identification [CASE:4347836] was created. I just noted this little puzzle on twitter by Brillant.org: \begin{align} A B C\\+ BCA\\ = CDE \end{align} Given that $A$ is even ...
3
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57 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 ...
3
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1answer
123 views

Solve returns solution that isn't (always) one

I was asking Mathematica to find the roots of $f(x) = a+\sqrt{x^2-b}$ and it returns $x = \pm \sqrt{a^2+b}$. These are however solutions only if $a\leq 0$ (there are no roots if a is positive since ...
3
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0answers
83 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 ...
3
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0answers
129 views

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 ...
3
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0answers
132 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 ...
3
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0answers
141 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. $a$ ...
3
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0answers
399 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 ...
3
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0answers
97 views

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

I call Reduce on the following simple system of inequalities ...
3
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0answers
92 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 ...
3
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0answers
80 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 ...
3
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0answers
97 views

Low accuracy while solving a multi-variable equation numerically

My question is as following: I was trying to make a function Vs2[r] with two parameters fit a set of conditions. Vs2[r]: <...
3
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0answers
296 views

How to solve partial differential equation

How to solve in Mathematica this partial differential equation: $0.5\frac{\partial t(x,y)}{\partial x}+1.5\frac{\partial t(x,y)}{\partial y}+t(x,y)=y\cdot \sqrt{1+x^{3}}$ with condition $t(1,y)=y+2$? ...
3
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0answers
187 views

Solving this system of nonlinear equations

Edit Interestingly, I realized solving my problem with $2n$ equations appeared to be more efficient than using mathematical results on the solutions to reduce the problem to $n$ equations (the $n$ ...
3
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0answers
259 views

NSolve doesn't work on an equation containing a numerical integral and constraints

I'm having trouble getting Mathematica to solve equations numerically. I know that its important to specify the type of variables for pattern testing (see e.g. here) but this doesn't seem to work. ...
3
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0answers
292 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 ...
3
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0answers
258 views

How can I improve the solution of my PDE?

I want to improve the last code to find a better solution for umi. For now I'm using only MaxStepFraction. Also, when I put no ...
3
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0answers
1k views

Solving a system of two nonlinear equations with many symbolic parameters

I have two nonlinear equations with two unknowns, $x$ and $y$, and many symbolic parameters, $a, b, c, d$. They look someting like: $\frac{1}{x}(1+x)^a (1-b)(cx+dy)=0$ $(\frac{1}{x^2}+b)(1+x)^d+(1+...
3
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0answers
505 views

Nonlinear FEM and FindRoot

I'm trying to develop a kind of nonlinear FEM application using mathematica to solve a bvp like the following: $$ \gamma(u') ~u^{iv} + 2 \gamma'(u') u''' u''+ u''^3 = f(x) $$ where $u = \tilde{u}(x)...
3
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0answers
431 views

Function with a sharp resonance which Mathematica fails to integrate. Why?

I'm a new user of Mathematica and I'm trying to use it to calculate the collisional cross-section as a function of energy for a given potential and decay rate. I know that the resulting function ...