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

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4
votes
4answers
987 views

recursively solve equation and saving the values

I am new to Mathematica. I am trying to recursively solve an equation and saving the values into a Table. Since I need the real solutions only I use ...
3
votes
1answer
193 views

Issue in ParallelTable after evaluating another function using NDSolve and FindRoot. What is wrong with this inverse?

I am trying to find the inverse of a function which is defined through NDSolve and NIntegrate. The question is pretty similar ...
3
votes
1answer
109 views

Aborts and beeps without error warning

I have a piece of code that generates a figure, performing a calculation to generate each pixel. At a certain resolution it runs fine, but after a high enough resolution it fails. Mathematica beeps ...
3
votes
1answer
184 views

Strange behavior of Reduce with a cubic equation

This equation: $(\frac{-a}{x})^2=\sqrt{\frac{1}{x}}$ at $a > 0$ and $x > 0$ has a clear solution $x=a^{4/3}$, doesn't it? However, ...
3
votes
1answer
409 views

Tips for efficiently solving large system coupled (nonlinear) ODEs

I'm trying to solve a system of nonlinear, coupled ODEs, where the governing equation for the $n-th$ ODE is of the form: $\sum_k^M Q_{nk} \ddot{a}_k -\sum_{\ell}^M\sum_k^M S_n(\ell,k) \dot{a}_{\ell} ...
3
votes
3answers
211 views

Speed up Eliminate

I have a set of trig equations, c1,c2,c3 are constants, I excepted the result is c1 c2 c3 r^2 + (c1^2 + c2^2 + c3^2 - 1) r + c1 c2 c3 == 0 but following code ...
3
votes
1answer
180 views

Finding the largest integer that cannot be partitioned in a certain way

I want to use Mathematica to solve the problem: Find the maximum $k$ such that $6x+9y+20z=k$ does not have a non-negative solution. I tried FrobeniusSolve. ...
3
votes
1answer
187 views

How can I get the general term of this recurrence equations?

Following is the recurrence relation: a[1] = 1; a[n_] := a[n - a[n - 1]] + 1 Array[a, 28] I tried to use RSolve, but it ...
3
votes
3answers
724 views

Solving Integrals

Here's a problem that I don't understand. f[x_] := Exp[Cos[3*x]] g[x_] := (1/3)*x^3 - x^2 + 2 When I try to find the limit: ...
3
votes
1answer
468 views

wrong use of _?NumberQ?

I am having trouble with a numerical exercise. Here's a simplified version of my problem. I define two functions to find the solution to two constrained maximization problems: ...
3
votes
3answers
401 views

Animate a position change along the curve for every iteration

I've only had few previous experiences on Mathematica before. So basically an entry-level question that harasses a rookie like me. I made the following attempt using bisection method to calculate ...
2
votes
3answers
208 views

Points of Intersection

How to numerically find points of intersection between pair of curves (Here,a circle and a parabola) ? Finding it a bit messy as, for a point on one curve, slope of the other is involved. ...
2
votes
1answer
123 views

Catastrophic loss of precision

while I am trying to solve the double integral in the range of 0 to Infinity (for both the integral) it give me the error Catastrophic loss of precision in the global error estimate due to ...
2
votes
1answer
286 views

Solving a system of nonlinear equations

The bellow set of equations has two answer sets for (α1, α2, α3, β1, β2, β3) respectively as following: (3, 1, 3, 1, 1, 1) & (3, 0.75, 3, 0.5, -1, 0.5) ...
2
votes
1answer
67 views

Find constants in a function? [closed]

Let's say I have a function f[x] with n constants, e.g. f[x] = c1 * x + c2*x^2 + ... + cn *x^n I also have n conditions to find those constants, e.g ...
2
votes
3answers
144 views

Solve works with numbers but not number stored in variable

I have the code: ...
2
votes
3answers
137 views

Is there a way to specify custom domains?

I want to solve for all solutions to the system of equations $a_1 a_2 a_3 b_4 + a_1 a_2 b_3 + a_1 b_2 + b_1 = 0$ and $a_1 a_2 a_3 a_4 = 1$ where the $a_i$'s and $b_i$'s take on values from $\{-1,1\}$. ...
2
votes
1answer
475 views

Solve[Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] breaks when “Reals” is added?

Mathematica solves this equation fine: Solve[ Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] // InputForm ...
2
votes
1answer
121 views

Compact form for domain ranges of many variables

When one sets up an equation to solve one often needs to specify conditions on the variables such as { x>0 && y>0 && z>0 } This is not ...
2
votes
1answer
703 views

How could I define a function as the solution of equations in Mathematica?

I have posed a specific question yesterday but it may be too trivial to answer. I think the question could be asked in a more general way so it is easier to answer. Then I could solve the original ...
2
votes
1answer
128 views

Finding the root of a nested function with small values

I have reduced an error in my program to this line of code: FindRoot[Nest[# (1 - #) k &, 1/2, 2^4] - 1/2, {k, 3.5}] It works for $2^1, 2^2, 2^3, 2^4,$ but ...
2
votes
1answer
133 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
2answers
447 views

FindRoot errors

I'm trying to solve a system of two equations in two variables for some range of parameter values. I use ContourPlot to see where I should look for a solutions and ...
2
votes
1answer
747 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
638 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 ...
2
votes
1answer
571 views

FindRoot Infinite expression 1/0 encountered error

I have 1 equation in 1 variable, which when I use Plot, looks like this: ...
2
votes
1answer
451 views

Inconsistent initial and boundary conditions

I have a 4th order nonlinear PDE with the following BCs and IC: ...
1
vote
1answer
94 views

strictly positive solution to $Ax=b$

How to find in mathematica one real strictly positive solution, if any, of $Ax=b$. A is rectangular matrix. Thanks
1
vote
1answer
100 views

handling division by zeros and line equations

today I was writing a code which takes some line equation and a circle equation,finds intersection points that are on $II$ and $III$ quadrants,draw a tangent line to circle from that point and then ...
1
vote
1answer
94 views

How do I link the txt file data sheet to mathematica and extract exact elements that I would like to use in solving for x? [closed]

I am trying to solve for a numerical solution for an equation which contains variables that evolves as index i incrreases. The actual equation that I am using to extract solution for x with an ongoing ...
1
vote
1answer
80 views

Numerically Integrating to find a Maximum using NDSolve

I am trying to numerically find an equilibrium (maximum) of a function using its differential. The following is a simplified version. ...
1
vote
0answers
69 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 ...
1
vote
1answer
111 views

Having trouble assigning the result of a Solve to a function

Can anyone see what is wrong with my syntax? It looks like I have successfully assigned the result of Solve to a function. I want Mathematica to return me an numeric value of the function ...
1
vote
2answers
234 views

intersection between function and plane

I try to solve a ODE system of equations and i want to plot the intersection of the 3D solutions with a costant plane. To do this i use the follow code: ...
1
vote
1answer
154 views

What is most efficient way to convert system of equations to collection of functions?

I have the type of system M.x = b, where M is a known matrix and b is a known vector. M contains many parameters, call the entire parameter set 'a', so M => M[a]. I want to be able to efficiently ...
1
vote
0answers
396 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 ...
1
vote
2answers
268 views

Approximate solution to system of polynomial equations

I'd like to solve approximately the following system of equations for $a_1$, $a_2$, $\alpha_1$ and $\alpha_2$ all real and nonzero: ...
1
vote
1answer
354 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
2answers
2k 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
0answers
61 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, ...
1
vote
3answers
296 views

Find a single max value

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1
vote
2answers
250 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
1answer
735 views

How can I understand the result Mathematica returns from DSolve?

I have solved an ODE using DSolve, but I have a problem with understanding the solution. In general the solution is in the form: ...
1
vote
1answer
200 views
1
vote
1answer
411 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 ...
0
votes
1answer
76 views

Solving A Series of Equations

I want to find the solutions of a series of equations as I stated in this question before. I understood how to solve the equations by maximizing the value of a variable but now I want to find the ...
0
votes
1answer
86 views

How can I resolve the insufficient memory to complete the computation problem for solving function with iterated variables?

I am trying to solve for a value x in a function where the variables varies with iterations of K. Also, there is one variable called "rvsum" which is updated with a certain formula as well. I have ...
0
votes
3answers
299 views

Solving One Equation with Two Variables

I am trying to solve an equation with two variables. It is the last step in the process of using the method of undetermined coefficients to solve a nonhomogeneous differential equation. The equation ...
0
votes
0answers
99 views

NDSolve producing an overdetermined system

I am trying to build the initial model for an electro-mechanical system that I will be running in a for-loop for various inputs and parameters. Currently, the code is as follows: ...
0
votes
0answers
45 views

How to obtain all minima? [duplicate]

If you Solve an equation, you obtain all solutions. But If you NMinimize a function, you only get one minimum. The question ...