Loading...
Please wait, while we are loading the content...
Similar Documents
Numerical Integration
| Content Provider | Scilit |
|---|---|
| Author | Bober, William |
| Copyright Year | 2013 |
| Description | The steps for calculating the integral, I, numerically by the trapezoidal rule are as follows: ◾ Subdivide the x-axis from x = a to x = b into N subdivisions, giving ∆x b a N = − (6.2) ◾ The area, Aj, under the curve in jth interval can be approximated as the area of the trapezoid bounded by (xj , fj , fj+1, xj+1), which is A f f xj j j= + + 1 2 1( )∆ (6.3) ◾ Repeat this process for all interval areas, giving A f f x A f f x A f f x A f fN N N 1 2 1 2 1 2 1 2 = + = + = + = + ( ) , ( ) , ( ) , , ( ∆ ∆ ∆ … +1 )∆x (6.4) ◾ We now sum all the interval areas (A1, A2, … , AN) to obtain the trapezoidal rule for evaluating the integral, I, which is I f x dx f f f f f x = ≈ + + + + + +∫ +( ) 1 2 1 2 (6.5) Example 6.1 Solve the definite integral, I, by the trapezoidal rule: I x x x dx= + − +∫ ( . . . )3 2 3 2 3 4 20 2 % Example_6_1.m % This program evaluates the integral by the trapezoidal rule % The integrand is: xˆ3+3.2*xˆ2-3.4*x+20.2 % The limits of integration are from 0-10. clear; clc; a = 0; b = 10; N = 100; dx = (b-a)/N; % Compute values of x and f at each point: Figure 6.1 Subdivision on x domain for trapezoidal rule. Book Name: Introduction to Numerical and Analytical Methods with MATLAB for Engineers and Scientists |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2012-0-08572-2&isbn=9780429101618&doi=10.1201/b16030-9&format=pdf |
| Ending Page | 248 |
| Page Count | 30 |
| Starting Page | 219 |
| DOI | 10.1201/b16030-9 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2013-11-12 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Introduction To Numerical and Analytical Methods with Matlab for Engineers and Scientists Hardware and Architecturee Curve Trapezoidal Rule Axis Clc Integrand Sum |
| Content Type | Text |
| Resource Type | Chapter |
