Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
2
votes
1answer
298 views
'not a valid variable' error when trying to solve 13 equations with 13 variables
I want to solve 13 variables by 13 equations. And here is my program:
...
2
votes
1answer
103 views
Computing the sign of the real part of eigenvalues in a 3D linearized system with 3 parameters
So I have this dynamical system given by:
$$
\left\{\begin{aligned}
x' &= a(y-\phi(x))\\
y' &= x-y+z\\
z' &= -by
\end{aligned}\right.
$$
where $\phi(x) = \mu x^3 - \nu x$ and $a,b,\mu,\nu$ ...
2
votes
1answer
157 views
How to solve equations self-consistently
I want to solve the following equation self-consistently. So,
H.u = e.u
{{1, d}, {d, 1}}.{u1, u2} = e.{u1, u2}
I guess an initial value for ...
2
votes
1answer
93 views
How to transform an expression using algebraical instead of pattern rules [duplicate]
I would like to transform rules algebraically. A very simple example would be: -
k^2 - 2 k x + x^2 /. {2*k -> 1}
This transforms to: -
$$k^2-2 k x+x^2$$
...
2
votes
1answer
141 views
Defining regions for `Exclusions`
I have the following function I want to plot in 3D (For simplicities sake we can say $a=5,b=-1,c=3$.)
...
2
votes
1answer
211 views
How to solve a symbolic equation with symbols in powers
I am trying to solve
$\dfrac{\rho\ ((1-b)\ \lambda _f\ \lambda _s\ P _A)^{\rho }}{b-1}+\dfrac{\rho \left(\dfrac{b\ \text{ps}\ x}{1-\text{ps}}\right)^{\rho
}}{b}=0$
in terms of $b$,
I ...
2
votes
1answer
77 views
InterpolatingFunction with growing Domain
I want to find roots of a function that is very slow to calculate (the function itself involves a bunch of FindMaxima) so I interpolate the function in a region where I think it likely the the root ...
2
votes
1answer
55 views
Differentiating with respect to vectors of unspecified length
Given a function defined by
f[x_,y_] := Sum[ x[[i]] (g[y[[i]]] - g[Total[y]] - Log[x[[i]]]), {i, 1, Length[x]}]
I can easily calculate the derivative for a fixed ...
2
votes
1answer
179 views
NDSolve two PDE plus one ODE, together
I have a couple of PDE (time and space/length) that are correctly managed by NDSolve, but to which I’m adding an ODE on which the acc “accumulates”, through time, a ...
2
votes
2answers
88 views
Why can't FindInstance find a solution to this equation?
FindInstance[680 == 1/3 2^m (-1 + 4^v), {m, v}, Integers]
FindInstance seems to be unable to find the integer solution $ {m = ...
2
votes
1answer
193 views
How can I solve an exponential inequality in Mathematica?
I would like to solve the equation:
A Exp[m t + s Sqrt[t] x - 1/2 s^2 t] >= K
with respect to x (which is in the exponent) ...
2
votes
1answer
216 views
Reduce/Solve an equation with symbols in powers
I am trying to solve the following equation with respect to x.
eqn = x^z + y == a;
But when I do
...
2
votes
0answers
61 views
Reducing exponential inequalities fails
I am quite stumped by this problem :
Reduce[ N^(x-y) <1 && N > 0 , x, Reals]
gives the expected result
...
2
votes
0answers
111 views
Nest for large value of n
I am working on a problem to find the Feigenbaum constant. In this problem I have to get $f^{2^n}(1/2)$ with $f(x) = kx(1-x)$. I use Nest to get $f^{2^n}(1/2)$ but ...
2
votes
0answers
74 views
Conditional statements in intial conditions?
This is potentially a daft question, but I thought I'd ask it; I have some material free to diffuse in a boundary between rn and ro; I've been able to get it working nicely for neumann type boundary ...
2
votes
0answers
89 views
differential equations with implicit functions
I have an ordinary differential equation that contains coefficient functions that depend implicitly on the independent variable via an algebraic equation. I am trying to go ahead and use NSolve to ...
2
votes
0answers
137 views
Solving $k\log(n) - k\log(k) \leq u$
How can I persuade Mathematica to help me find solutions to the inequality
$k\ln(n) - k\ln(k) \leq u$ over the reals, assuming $u \geq n \geq k \geq 1$.
When I evaluate
...
2
votes
0answers
106 views
Am I entering this 2-variable recurrence correctly?
I'm trying to solve this recurrence with two variables.
...
2
votes
0answers
139 views
FindRoot - Speed and errors
I am using FindRoot[] to solve a complicated equation. It seems I get the correct answer even though I get errors about an ...
2
votes
0answers
83 views
Why cant Mathematica solve this equation? [duplicate]
Possible Duplicate:
Can Reduce *really* not solve for x here?
Why cant Mathematica solve this equation?
...
2
votes
0answers
173 views
Numerically/Analytically Solving a System of Equations
I have $6$ functions $f_i(x,y,z)$, $(i = 1, \ldots, 6)$ in three variables $x,y,z$, and I would like to find a simultaneous instance of these variables, say $(x_0, y_0, z_0)$, such that $f_i(x_0, y_0, ...
2
votes
1answer
307 views
Inconsistent initial and boundary conditions
I have a 4th order nonlinear PDE with the following BCs and IC:
...
1
vote
2answers
131 views
Is there a better way to get the eight points of intersection?
I want to get the eight points of intersection from the equations 2 Abs[x] + Abs[y] == 1 and Abs[x] + 2 Abs[y] == 1. To solve ...
1
vote
2answers
222 views
1
vote
2answers
114 views
Using FindRoot with an interpolating function
This question bears resemblance to a few other questions on mathematica.SE about finding points of intersection of crossing curves. I know that the guidebook of numerics has an entry about the whole ...
1
vote
1answer
237 views
2 non-linear equations with 2 unknowns which I cannot solve
I have the following equations and I would like to solve them in Mathematica anyway. Numerical results are very much welcomed. However, when I use the command ...
1
vote
3answers
371 views
Conditional expression
How do I evaluate a conditional expression in order to convert the solutions that are in terms of $x$ to a new variable $c$ depending on $x$? The conventional method I have been using with eliminate ...
1
vote
1answer
92 views
Substituting solution from Solve into the equation and making a plot
I want to solve an equation and substitute it into a Plot expression. My code looks something like this
a[b_, x_] := bx + 1;
sol = Solve[(1 + b)x + 1 == 0, b]
I ...
1
vote
1answer
127 views
Comparing two symbolic expressions
Does Mathematica provide any way to compare two symbolic expressions and find which is the greatest? For example, I want to find which is the greatest of ...
1
vote
1answer
369 views
FindRoot inside Table
(MWE at the end of the post)
I need to solve a non-linear equation $f(y;x_1,x_2,..,x_5)$ in one variable $y$ and then compute 4 new output expressions, for over 60 different initial parameter inputs ...
1
vote
2answers
99 views
Count and plot the number of solutions in an interval
I have equations depending on one or more parameters and I want to find and plot the regions in the parameters space in which there are a specific number of solutions.
For definiteness let's ...
1
vote
1answer
117 views
Solving Intervals
In a recent question I posed, it was noted that by design, Sqrt[ blah] only returns the positive branch, even though we might want to obtain all possible symbolic solutions. So, taking care to avoid ...
1
vote
1answer
345 views
Forcing FindRoot to return only real solutions
FindRoot documentation reports that if the Equation and the initial point are reals, the solutions are searched in the real domain.
However, in the following case I ...
1
vote
1answer
325 views
Linear Solve with Modular Arithmetic
I am interested in using LinearSolve[m,b] which will find a solution to the equation $m.x=b$, where I am in mod 2 arithmetic. Is there any way to perform this ...
1
vote
2answers
207 views
Replacing variable in an equation with an Interpolating function polynomial and plotting residual
I was trying to plot the residual for the solution of my PDE. However, I was unsure about a couple of things.
I imported the data and created an Interpolation polynomial with ...
1
vote
2answers
568 views
Find the dimensions of a cylindrical can that will minimize the cost of the material
A cylindrical can is to be made to hold 1 L of oil. Find the dimensions
that will minimize the cost of the metal to manufacture the can.
This is a standard calculus problem.
The volume of the ...
1
vote
1answer
80 views
Prandtl-Meyer function
I'm trying to solve for Mach number based on the given Prandtl-Meyer function, however I keep getting odd error.
Here is my code:
...
1
vote
3answers
194 views
1
vote
1answer
62 views
Calibrating Precision in calculations
As the title says, I encounter an irritating problem which has to do with the accuracy or the precision used in the calculations. To be more specific, I have the following code:
...
1
vote
1answer
99 views
Forcing evaluation of ArgMax
How to force evaluation of ArgMax before its output gets used in Solve?
Background: I'm trying to solve for the Nash ...
1
vote
1answer
131 views
Using 'Reduce' to solve a set of inequalities, specified by a list
I have a two lists $LHS$ and $RHS$, both of size $n$. I want to solve a system of inequalities of the form:
$$LHS[1] \leq RHS[1]$$
$$LHS[2] \leq RHS[2]$$
$$LHS[3] \leq RHS[3]$$
$$\vdots$$
...
1
vote
1answer
231 views
Using previous two solutions as a start point in FindRoot
I need to solve a sequence of equations and I want the starting point of each new FindRoot to be the solution of the earlier FindRoot, increased or decreased by a a bit in the following way:
Some ...
1
vote
2answers
82 views
Rearranging an equation with the sine function in it [closed]
When I evaluate Solve[a==Sin[b*c], b] to rearrange the following for $ b $:
$$ a = \sin(bc) $$
I get the following result from Mathematica:
$$\begin{align*} ...
1
vote
1answer
101 views
1
vote
1answer
125 views
How can I get the solution of complicated implicit function?
The question is what is the method to solve the implicit function has real and imaginary number.
For example, The function is F(x,y)=(-I*x + 2*y^2)^2 + x^2 - 4*y^4*Sqrt[1 - I*x/(y^2)].
Although I ...
1
vote
3answers
283 views
equation solving problems
I have some equation:
$$
veq=-2-lr-l^2r+2(r+ir^3\omega) v' + (-2+r)r^2v'^2 + (-2+r) r^2 v''==0
$$
or in Mathematica form:
...
1
vote
1answer
1k views
solve non-linear system of equations
I have a system of equations and I want to solve it to get x, y
$$\begin{cases} u= C_{1}+(x-C_{1})(1+k_{1}((x-C_{1})(x-C_{1})+(y-C_{2})(y-C_{2}))) \\ \\ v= ...
1
vote
1answer
64 views
How to get a solution set of a nonlinear system of equations?
I'm trying to find the solution set of {x, y} variables for the following system of equations:
...
1
vote
1answer
172 views
solving a cubic equation
I need to find the minimum $r$ and the maximum $k$ of the following cubic equation for which there does not exist three distinct real roots.
$rx^3-rkx^2+(r+k)x-rk=0$.
Is it possible to find such $r$ ...
1
vote
1answer
141 views
Is my system too complicated for Solve?
I am trying to solve a system of three nonlinear equations using Mathematica. Solve takes forever to run and never solves my system of equations. Is my system too ...
