# Questions tagged [numerical-methods]

Algorithms which solve mathematical problems by means of numerical approximation (as opposed to symbolic computation).

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590 views

### Calculating pi by adding areas of thin rectangles

I wrote a small program for fun to try to prove Pi by taking a certain precision and radius and using it to calculate the area of the circle. My method should be giving me an area that is just ...
591 views

### Visualizing Newton-Raphson method for finding zeroes of a function

I have created a program to visualize the working of Newton-Raphson method to find the zeroes of a function: newton.m: ...
3k views

### Implementation of exp function in C using Taylor Series expansion

I am trying to write code to calcultate ex using: $$e^x = \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots$$ This is the code I have, which works ...
839 views

### 1D shock tube problem written in Fortran

I have written a simple Euler solver for the 1D shock tube problem. Eventually, I plan to extend this code to solve the full 3D compressible Navier-Stokes equations. Therefore, I want to start with ...
2k views

### Linear Interpolation C++

I have to write a collection of methods for performing linear, bilinear and trilinear interpolation. I have also to write some tests to show that interpolation is exact for polynomials (which should ...
143 views

### Square root calculation in Scheme (SICP Exercise 1.7)

I have done exercise 1.7 in SICP (calculate square root precision when change in guesses is under a certain value), but I am calling the change-in-precision function twice in each iteration, which ...
147 views

### atof revisited

In an answer to this question I mentioned best effort. Here I try to explain what I meant. Please keep in mind that the implementation is intentionally incomplete (missing features such as ...
93 views

### Integer square root

This essentially performs the same function as exact-integer-sqrt in math.numeric-tower. ...
152 views

### Computing the double Integral using MonteCarlo techniques using Julia

I decided to try and learn Julia for doing scientific computing, and I decided to tackle the problem of finding $$\int_{D_{\frac{1}{4}}} x^4 + y^2 dA$$ where $D_{\frac{1}{4}}$ is the part of ...
606 views

### Linear shooting method to solve a B.V.P

I have wrote a code to approximate the solution of a boundary value problem: x'' = p(t)x'(t)+q(t)x(t)+r(t) x(b) = beta in [a,b] by using Runge-Kutta method ...
2k views

### Double integral solver in TI-84

Here's a program I made for estimating a double integral over a general region. It's pretty accurate, but it's VERY, VERY slow. (Getting an accurate enough result takes about 30 seconds) Here's the ...
246 views

### Approximating π via Monte Carlo simulation

Inspired by a tweet linked to me by a friend and a Haskell implementation by her for the same problem, I decided to try my hand at approximating the value of π using everything in the Haskell standard ...
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### Computing integer square roots in Java - follow-up

(See the previous iteration.) My two previous methods for computing the integer square root of a number $N$ ran in the $\mathcal{O}(\sqrt{N})$ worst case time. Now I have added a method (...
495 views

### Gamma function in Rust

The gamma function is one of a couple nice continuous extensions to the traditional factorial function. I used this Python program as a reference, which in turn, uses this Ada program. As the Ada ...
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### Reinventing the Math Functions

Just for practice in the mathematical side of programming, I decided to rewrite the math functions, with the addition of the root() function, which the Math library ...
375 views

### Newton's Method Polynomial solver in Ruby

I am learning Ruby programming from "Learn Ruby the Hard way" and I am doing the "Ruby koans". I have heard a little bit about "Idiomatic" Ruby but I don't know much about it. How can I make it more ...
191 views

### Simple neural-network simulation in C++ (Round 4)

You may want to take a look at Rounds 1, 2, and 3, though that isn't necessary for understanding what's below. The major change since Round 3 is that my code is much cleaner and I'm including ...
221 views

### Simple neural-network simulation in C++ (Round 3)

As I mentioned at the end of my Round 2 answer, I've needed to expand my code in order to produce faithfully the data needed for Figure 1 of this paper. Unfortunately, the updates have made my script ...
215 views

### Simple neural-network simulation in C++ (Round 2)

Intro Yesterday I posted this question. Since then, I've updated my code to incorporate these suggestions. I've also removed the dependence on C++11. Finally, I've made the following changes that ...
2k views

### Simple neural-network simulation in C++

The C++ code below simulates the timecourse of the membrane potential (V) of a population of 128 leaky integrate-and-fire ...
92 views

### Golden Section Search in Lisp

I implemented the golden section search algorithm recursively in Lisp. My code is: ...
64 views

### Decorator for setting up bracketing rootfinding functions

I'm looking for comments on the use of decorators for the following problem (validating initial guesses for bracketing rootfinding methods), as well as any other comments you might have on the design ...
6k views

### Implementation of Brent's Algorithm to find roots of a polynomial

I made a program that contains a root-finding algorithm for polynomials as a function and contains 3 test polynomials. The algorithm is Brent's method and is based entirely off the pseudocode from ...
1k views

### Root-finding by iterated bisection

Both of the following code give the same result. But I'm not sure where should I put the raise statement. ...
31 views

### Iterative procedure to get 3D coordinates from distance constraints

Imagine you have a series of n points randomly generated in a box in 3D space. You also have a list of distance bounds, e.g. points 5 and 3 should be between 1.0 and 2.0 Angstroms apart. There are ...
1k views

### Buffon's Needle experiment

I was working on a program that simulates the Buffon's Needle experiment. If anyone is not familiar with it, a Wiki link is provided - Buffons's Needle The point of Buffon's experiment is to find ...
194 views

### Monte Carlo Pi (MASM)

I'm currently trying to brush up on my assembly skills and, being at the FPU section of the tutorial, I implemented a very basic version of a Monte-Carlo-Algorithm to compute pi. I deliberately use ...
97 views

### Calculating e^x by math.h and by own means

For this program, the user needs to enter an exponent and the program will calculate $e$ (Euler's number) to the power of the exponent the user inputs. This is done by two ways: By the math.h ...
419 views

### Utility Method to find the Square root of a number

Utility to calculate the square root of a number. The method also accept an epsilon value, which controls the precision. The epsilon value could range to any number including zero. I am expecting a ...
1k views

### Poker Odds Calculation with Monte Carlo

I have created an Odds Calculator in Java. The program gives me the odds, but I want to make sure that they are correct. Maybe someone can tell me a calculator I can compare my results with or knows ...
557 views

### Functional abstraction to find nth root of a number - Newton raphson

Below is the solution: ...
378 views

### Terry Feagin's 10th order explicit Runge-Kutta method

The following Julia code implements Terry Feagin's 10th order explicit Runge-Kutta method (a more accurate cousin of RK4). Though the structure of the code is quite simple (i.e. no cyclomatic ...
117 views

### Summation for π [closed]

I was going through my Java book's exercise solutions and comparing and incorporating the author's techniques into my repertoire. Most of the time, my approach is identical to the author's. When it ...
2k views

### Iterative equation solver in Python

In order to solve a equation where the left hand side appears under an integral on the right hand side:  B(p^2) = C\int_0^{p^2}f_1\left(B(q^2),q^2\right)\mathrm{d}q^2 + C\int_{p^2}^{\Lambda^2} f_2\...
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### How can I make this Euler/RK4 implementation more elegant?

One of the things that I'm doing to teach myself is converting some numerical methods from existing Python code (they seem to me to lend themselves to functional programming quite well). I'd like to ...