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

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1answer
58 views

How to change the expressions in terms of a specific variable?

I have a series of analytical equations: ...
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64 views

How to find Pauli matrices

I wanted to find the Pauli matrices, so i wrote down this code: z = {{a, b}, {c, d}} i = {{1, 0}, {0, 1}} Solve[z.z == i, {a, b, c, d}] and mathematica gave me ...
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88 views

Mathematica reading my mind - Solve knows which variable to solve for

I was checking some of my algebra with the following code; ...
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48 views

Equation solving: Solve returns a periodic solution

I have a very simple trigonometric equation, that I've been trying to solve for a variable for a few hours now: (I couldn't find how to correctly format this) ...
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50 views
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42 views

Input `Reduce[Mod[a + x, l] == 0, x]' and output `x == -a + kl`?

Reduce[a + x == k l && k > 0, x] (* k > 0 && x == -a + k l *) I think a + x == k l and ...
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0answers
121 views

Equation Solving

As I stated in this question I want to solve a series of equations while setting some rules such as q[2]->1 or q[2]->3*10^-4. However, what should I do if I want to set another rules to my input? I ...
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159 views

NDSolve: Equation with interpolating function [closed]

I have a question regarding DSolve and NDSolve functions in Mathematica 10. For instance, I'd like to solve an ODE: ...
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39 views

Resolve not accepting equations involving factorial

If I take , Resolve[ForAll[x,x!>=0],Integers] True But if I make slight modification, ...
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0answers
58 views

Help inteprete the solution given by reduce

i am trying to solve for the a2 in the below equation on Mathematica ...
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1answer
34 views

problem on returning value of function as a list using if

today i was writing a function for my project using mathematica that gives a line equation in form of $y=mx+b$ and a circle equation in form of $x^2+y^2=r^2$ and finds the intersection point which is ...
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86 views

Using NMinimize to solve the Multi Commodity Flow problem

I have the following optimization problem and I was hoping to solve it with NMinimize. Unfortunately, I don't get the desired result. I would like to get an optimal vector for $d_{e}$. This is how ...
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0answers
94 views

Numerical solution to two non-linear coupled differential equations [closed]

I am trying to solve two differential equations representing the position of an object in space. I have specified arbitrary initial conditions. ...
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0answers
55 views

Creating a matrix from a list of simultaneous equations

I have a list of n simultaneous equations of the form, w A[n] = (K[n,n+1]+K[n-1,n])A[n] - K[n,n+1]A[n+1] - K[n-1,n]A[n-1] ...
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98 views

Comparing two ways of fitting systems of ODEs to data

I'd like to ask you if you see any difference between the two following ways of estimating parameters. Given my system of ordinary differential equations that I want to use to find the values of all ...
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0answers
97 views

Stability region of midpoint method using Solve and RegionPlot

I've been trying to obtain the stability region in the $(\lambda_R, i\lambda_I)$ plane of the midpoint rule $$y_{n+1}= y_{n-1}+2h\dot{y}_n,$$ for the model problem $\dot{y}=\lambda y$. The roots for ...
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1answer
100 views
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127 views

Code for solving numerically an integro-differential equation

First of all, I want to greet the community. This is my first question, but I hope I will be able to help answering others members questions, although I am quite new working with Mathematica. I would ...
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0answers
34 views

Determine Functions Given Data Points [duplicate]

Is it possible for Mathematica to solve for f(x,y) = 0 such that {x,y} contains {{0,0.5}, {1,0.5}, {0.6,0.8}, {0.4,0.2}} ? Do we need to specify f(x,y) first ? ...
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0answers
123 views

Finding Values of All Nine Constants in q-hypergeometric Equation

I suspect that an identity of the form $$\sum_{j=-n}^{j=n}(-1)^jq^{j(5j+1)/2}=\sum_{r=0}^{n}f_{ar+bn+c}(-1)^{n-r}q^{(n-r)(dr+en+f)/2}\frac{(q;q)_{gr+hn+j}}{(q;q)_{n-r}}$$ for $a, \dots , j$ integer ...
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134 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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0answers
26 views

Minimizing roots of a transcendental equations [duplicate]

I'm trying to use the solution of FindRoot with parameters for further calculations. Annoyingly enough it always gives me trouble with replacing the parameters. As an example I'm attaching a simple ...
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0answers
33 views

Correct use of Mathlink's MLGetRealList

I am attempting to use Mathlink from C. I have managed to return single values from mathlink to my c program, but I am having trouble with lists. Consider the Mathematica operation: ...
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37 views

How can I select two lists from a list of lists so that I receive the system of equations has only rational solutions?

I want to make a sytem of equations has the form $$\begin{cases} a_1x^2+b_1y^2 + c_1xy+d_1x + e_1y+3=0,\\ a_2x^2+b_2y^2 + c_2xy+d_2x + e_2y+3=0. \end{cases}$$ so that the given system of equations has ...
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1answer
88 views

How do assign an interval of values to a variable in order to use them in a function?

From my code (below) I have K1 and K2 set to zero in order to test this numerical method. However, K1 is on an interval from 0 to 32, and K2 is on an interval from 0 to 8. I would like to know if ...
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22 views

Solving a pair of recurrence relations [duplicate]

Why does this RSolve[{y[t] == a*y[t - 1]}, {y[t]}, t] work, while this ...
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0answers
75 views

Finding undetermined coefficients with boundary conditions

I have 2 equations which are; To[x_] := c1 E^(-a1 x)/2 + c2 E^(a1 x)/2 + a2 Tu[x_] := c3 E^(-a3 x)/2 + c4 E^(a3 x)/2 Tu equals almost zero ...
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106 views

What are the hidden specifications for FindRoot

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system" (or a nonlinear equation I ...
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1answer
284 views

Solving a System of four equations (with logs) [closed]

I am trying to solve a system of four equations in four variables. I have read a number of threads on similar issues and tried to follow the suggestions. But I think it is a bit messy because of the ...
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0answers
151 views

Calculating derivatives of roots of equation

I am interested in calculating how the roots of an equation change as one of the variables does, when the equation is evaluated numerically rather than symbolically. I have edited this code to be ...
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0answers
58 views

Gram Schmidt Process for functions [duplicate]

I want to implement the Gram Schimdt procedure to the space of functions in the following form \begin{align}‎ ‎R(y,x)=\left\{‎ ‎\begin{array}{ll}‎ f(x,y), ‎& y\leq x\\ \\‎ g(x,y), ‎& y>x‎ ...
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1answer
358 views

Unable to solve a set of equations with Solve

I'm trying to solve the following equation using Mathematica 9.0.1.0 : ...
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0answers
571 views

Solve[] unexpectedly giving empty solution sets for extremely large problems

I was calculating the set of lattice vectors in $\mathbb{Z}^4$ which have taxicab norm $r$. For example, executing ...
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0answers
167 views

No response from DSolve

Using optimal control theory, I am trying to find the optimal paths of d and k such that they will maximize profit as given by lc: ...
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313 views

Differential equations: How do I solve a delay differential equation with 0-1 variables

How do I solve the following non-linear, delay-differential equations using Mathematica under the assumptions $$p(t) = 1 ,\; y(t) > k$$ $$p(t) = 0,\; y(t)<= \ k$$. $$ \frac{dw}{dt} = ...
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0answers
354 views

Why DSolve and NDSolve give different answer

Consider these code, which solve the same equation using DSolve and NDSolve, why do they give different answer? Which one is ...
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1answer
77 views

Find the point that holds a given property

I have a normal distribution with mean 106, and a standard deviation of 8. I'm being asked to find the point that has the property that 25% of these values have this value or lower. What I've ...
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0answers
280 views

Solving asymptotic equations

Let's say I have several equations that have solutions given as a negative series $$y(t,x)=\sum_{n=-1}^\infty a_n(t) x^{-n}=a_{-1}x+a_0+a_1x^{-1}+\mathcal{O}(x^{-2})$$ My equations look like ...
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80 views

Simple Solve example fails: why? [duplicate]

Solve is an amazing tool, but sometimes it doesn't work in the way I expect it to. The particular instance that is confusing me right now is this: ...
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1answer
252 views

Gram Schmidt inner and outer products

I know the Gram-Schmidt orthogonalization generates an orthonormal basis from an arbitrary basis. I need help with: Write a program that inputs a list $\{b_1,\dotsc,b_n\}$ of linearly independent ...
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40 views

How can I access numerical values of variables calculated with Solve? [duplicate]

I am trying to calculate some thermodynamical cycles so I often use lists with equations. Here's a simple example: ...
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117 views
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182 views

Having Mathematica solve or help solve a set of 8 equations

There is a set of DDE's that arise in leukemia dynamics and I'd like to find the equilibrium points of the system by setting all of the derivatives equal to zero. The system can be described in ...
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0answers
70 views

Is it possible for Mathematica to give the step by step process of Reduce command? [duplicate]

Input: Reduce[3 x^2 - 2 a x + a^2 - 1 >= 0 && x > a, x] // TraditionalForm Output: ...
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203 views

Making simultaneous equation solving more efficient

I am trying to solve a system of several simultaneous equations that have been generated by a series of modules and functions, using this module: ...
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0answers
287 views

Why is a bump function making NDSolve take forever to solve?

I am attempting to solve a system of relatively complicated elliptic PDEs via a relaxation technique. In particular, I am trying to solve $\textrm{div} LW = S$ where $S$ is some vector and $L$ is the ...
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0answers
65 views

Finding Maximum Root [duplicate]

How can I find the greatest root for a polynomial if the polynomial degree is very large. One way is using NSolve. This command can find all roots in numeric. Then, ...
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0answers
93 views

Solving for vector elements in a function to which the vectors are not passed explicitly

I want to define a function which takes in two integers (indicating the lengths of 2 vectors), and solves a simple set of expressions at a set of points to find all the values in both the vectors. so ...
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0answers
248 views

Automatic inverse for Lambert’s Azimuthal Equal-Area Projection

I’m interested in finding closed-form inverses for map projection equations in general (of course, this is not always possible). I’m hoping Mathematica can help me with some of the trickier ones. As ...
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0answers
720 views

Calculating the mean curvature of a surface - suggestions

I am attempting to calculate the mean curvature [1, 2] of a surface defined by a function of x and y. My function is rather ...