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

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2
votes
1answer
88 views

Potential flow over cylinder with FEM: Pressure field is flipped

Much in the fashion of a few problems already answered on Mathematica.SE (1, 2), I am trying to solve the Laplace equation in velocity potential $\phi$ to simulate irrotational, inviscid flow over a ...
0
votes
0answers
26 views
0
votes
1answer
64 views

Multivariate Equation solving [closed]

I have the following equation: r^(1 + Rho) - r^Rho (-1 + Mu) - z Rho == 0 I searched the list but I couldn't come up with a solution. Any help is appreciated. ...
1
vote
0answers
53 views

Use Solve[] with Bessel, gamma, and hypergeometric functions?

I need to find values of {a,b,c} such that the 0th, 2nd, and 4th order moments of f[x]=Exp[-ax^4 - bx^2 - c] will equal respectively {1,2,10}. I didn't really expect this to work, and it didn't: ...
2
votes
1answer
128 views

Visualizing how the zeros for this function change as its input parameter changes?

I'm trying to explore how the zeros of a certain parameterized function change as its parameter changes. ...
0
votes
1answer
33 views

Finding solution of equation with differentials [closed]

I am trying to find the point of maximum exponential curvature, where the exponent equation is: y = 0.2e^(0.4x) I know the equation for this point is: k = y'' / [(1+y')²]^(3/2) How can I code this ...
0
votes
1answer
33 views

How do I assign the solutions of an equation to separate variables? [duplicate]

I'm a beginner to Mathematica. Here's my question. I'd like to store the output(s) of a Solve command to variable(s) that can be manipulated later. For example, I would like x1 and x2 to be the two ...
2
votes
1answer
76 views

Exclusions found but Solve and Reduce don't find exclusions

I have the following from Stan Wagons Mathematica in Action. ...
4
votes
1answer
130 views

Dealing with 6 VERY large equations. Am I doing this correctly, and can I expect a solution?

I'm new to Mathematica, but so far, everything seems straight forward and intuitive, which is really nice. However, I've come to use this software since I have to show a rather nasty 3x3 matrix is ...
2
votes
1answer
38 views

“Reduce” an expression in terms of a sub-expression

Newbie here. I've been trying to use Reduce to solve a rather long equation. The evaluation has been running for more than hour now, but still hasn't stopped. I've got an inkling that if I were to ...
9
votes
2answers
473 views

Is there a way to symbolically invert a piecewise function

I have a piecewise function that is continuous and strictly monotonic, like this: f[t_] = Piecewise[{{t/4, t < 0}, {t/2, t < 3}, {3/2 + (t - 3)*3, True}}] ...
0
votes
1answer
62 views

Why does this evaluate to {}?

I'm stuck with what seems to be an extremely simple issue, still, I just can't seem to find the solution or even the cause of the problem. So my issue is that I have the following surfaces: ...
5
votes
2answers
90 views

How to stop solving after one solution is found?

With[{P = 12}, Solve[{a^2 + b^2 == c^2, a + b + c == P, 0 < b <= a, c > 0}, {a, b, c}, Integers]] {{a -> 4, b -> 3, c -> 5}} ...
3
votes
1answer
67 views
0
votes
1answer
68 views

Solving an NODE in series

How can I solve this NODE in series y''[x]^2 + (1/2)*y'[x] + (1/2) y[x] == p x + q. `p` and `q` are constant. But do not know how to actually solve it with ...
13
votes
1answer
315 views

ToNumberField won't recognize Root as an explicit algebraic number

Bug fixed in 10.0.0 In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an ...
2
votes
0answers
57 views

Is FindRoot wrong about its WorkingPrecision?

I noticed an odd mismatch between the behaviors of NDSolve and FindRoot. If you give NDSolve an equation of a certain precision, say 20, and tell it to use a higher WorkingPrecision, say 30, it will ...
4
votes
1answer
280 views
0
votes
1answer
55 views

how to simplify -1 to shared power (produced by Solve)

I want a real solution to look real. But this solution does not: ...
3
votes
1answer
70 views

Solve problem: Inconsistent or redundant transcendental equation

I would like to mechanically Solve[a y == (1 - a) x && u0 == x^a y^(1 - a),{x,y}], given 1>a>0 and u0>0. The emphasis is on mechanically: I know it is ...
5
votes
2answers
130 views

How to find an estimated root efficiently with binary stochastic estimation of the function?

I am trying to construct certain nice geometric patterns, and one particular feature I'm trying to optimize is the balance of black and white corresponding to point being inside, or outside a ...
5
votes
2answers
2k views

Solving a trig equation

I am trying to find an explicit solution to a trigonometric equation. It is running for a long time and I didn't get any result, but Maple solves it quickly. Why ? ...
-2
votes
1answer
45 views

Generic approaches for multivariable polynomials across different domains [closed]

Mathematica newbie here. So I don't have a lot of time to read through the whole library of functions and language rules. So I'm trying to settle in on generic ways of doing the math that I'm going to ...
4
votes
2answers
266 views

Can I solve a certain equation?

Neither Mathematica nor Wolfram|Alpha can resolve the following. How else can I reach a solution? Reduce[(1 + x)^(2/m) - (1 - x)^(2/m) == (1 - x^2)^(1/m), x]
2
votes
2answers
140 views

Plotting the solution of a cubic equation against a coefficient in the equation

I have to plot the solution of the following equation against the coefficient $L$. Since it's a cubic equation, I'd like to filter out the real solution first and plot that then. The equation is $L ...
2
votes
1answer
63 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
94 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
132 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
71 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
192 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
175 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
90 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
102 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
270 views
15
votes
2answers
2k 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
476 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
83 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
98 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]}] ...
2
votes
3answers
176 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
154 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
416 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 ...
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 ...
2
votes
1answer
72 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
66 views

Reduce Inequality

How can I reduce the inequality in terms of modulus of alpha. ...
2
votes
1answer
85 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: ...