How to resolve the algorithm Numerical integration step by step in the Ursala programming language

Published on 12 May 2024 09:40 PM
#Ursala

How to resolve the algorithm Numerical integration step by step in the Ursala programming language

Table of Contents

Problem Statement

Write functions to calculate the definite integral of a function ƒ(x) using all five of the following methods: Your functions should take in the upper and lower bounds (a and b), and the number of approximations to make in that range (n). Assume that your example already has a function that gives values for ƒ(x) . Simpson's method is defined by the following pseudo-code:

Demonstrate your function by showing the results for:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Numerical integration step by step in the Ursala programming language

Source code in the ursala programming language

#import std
#import nat
#import flo

(integral_by "m") ("f","a","b","n") =

iprod ^(* ! div\float"n" minus/"b" "a",~&) ("m" "f")*ytp (ari successor "n")/"a" "b"

(integral_by "m") ("f","a","b","n") =

iprod ^(* ! div\float"n" minus/"b" "a",~&) ^H(*+ "m"+ -:"f"+ * ^/~& "f",~&ytp) (ari successor "n")/"a" "b"

left       = integral_by "f". ("l","r"). "f" "l"
right      = integral_by "f". ("l","r"). "f" "r"
midpoint   = integral_by "f". ("l","r"). "f" div\2. plus/"l" "r"
trapezium  = integral_by "f". ("l","r"). div\2. plus "f"~~/"l" "r"
simpson    = integral_by "f". ("l","r"). div\6. plus:-0. <"f" "l",times/4. "f" div\2. plus/"l" "r","f" "r">

#cast %eL

examples = <.left,midpoint,rignt,trapezium,simpson> (sqr,0.,pi,10)

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