-
Notifications
You must be signed in to change notification settings - Fork 0
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
Showing
2 changed files
with
117 additions
and
0 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,117 @@ | ||
| ' runs on https://dotnetfiddle.net/8K7fkp | ||
|
|
||
| Imports System | ||
|
|
||
|
|
||
| ' ================================================================================== | ||
| ' Main program to test BISECTION.BAS | ||
| ' ================================================================================== | ||
| Public Module Test_Bisection | ||
| Public Sub Main() | ||
| Dim Halves As Integer, maxit As Integer | ||
| Dim a As Double, b As Double, eps As Double, root As Double, fa As Double, fb As Double | ||
|
|
||
| maxit = 99 | ||
| eps = 0.0005 | ||
| a = 0.0 | ||
| b = 4.0 | ||
|
|
||
| fa = FUNC(a) | ||
| fb = FUNC(b) | ||
| If fa * fb > 0 Then | ||
| Console.WriteLine("No root in interval (a,b). Change the interval.") | ||
| Return | ||
| End If | ||
|
|
||
| Call Bisection(a, b, maxit, eps, root, Halves) | ||
|
|
||
| Console.WriteLine(New String("=", 44)) | ||
| Console.WriteLine("! Root is {0,14:F8} after {1} bisections !",root, Halves) | ||
| Console.WriteLine(New String("=", 44)) | ||
|
|
||
| root = (a * fb - b * fa) / (fb - fa) | ||
| Console.WriteLine() | ||
| Console.WriteLine(" *** Root (with linear interpolation) = {0,14:F7}", root) | ||
| Console.WriteLine(" *** Clossness to the root, Abs[f(root)]= {0,14:E4}", Math.Abs(FUNC(root))) | ||
| Console.WriteLine() | ||
| End Sub | ||
|
|
||
| Public Sub Bisection(ByRef a As Double, ByRef b As Double, ByVal maxit As Integer, ByVal eps As Double, ByRef root As Double, ByRef Halves As Integer) | ||
| ' ================================================================================== | ||
| ' CODE4.1-BISECTION.BAS. A Basic (VB) Sub implementing Pseudocode 4.1. | ||
| ' | ||
| ' NUMERICAL METHODS FOR SCIENTISTS AND ENGINEERS: WITH PSEUDOCODES | ||
| ' First Edition. (c) By Zekeriya ALTAÇ (2024). | ||
| ' ISBN: 978-1-032-75474-1 (hbk) | ||
| ' ISBN: 978-1-032-75642-4 (pbk) | ||
| ' ISBN: 978-1-003-47494-4 (ebk) | ||
| ' | ||
| ' DOI : 10.1201/9781003474944 | ||
| ' C&H/CRC PRESS, Boca Raton, FL, USA & London, UK. | ||
| ' | ||
| ' This free software is complimented by the author to accompany the textbook. | ||
| ' E-mail: [email protected]. | ||
| ' | ||
| ' DESCRIPTION: A Visual Basic module to find a root of a nonlinear equation in [a,b] | ||
| ' using the Bisection method. | ||
| ' | ||
| ' ON ENTRY | ||
| ' [a,b] :: Initial search interval (it must bracket one root); | ||
| ' maxit :: Maximum number of iterations permitted; | ||
| ' eps :: Convergence tolerance. | ||
| ' | ||
| ' ON EXIT | ||
| ' halves:: Number of halves realized; | ||
| ' root :: Computed approximation for the root. | ||
| ' | ||
| ' USES | ||
| ' ABS :: Built-in Intrinsic function returning the absolute value of a real value; | ||
| ' | ||
| ' ALSO REQUIRED | ||
| ' FUNC :: User-defined external function providing the nonlinear equation. | ||
| ' | ||
| ' REVISION DATE :: 11/20/2024 | ||
| ' ================================================================================== | ||
| Dim p As Integer, interval As Double, fa As Double, fb As Double, xm As Double, fm As Double | ||
|
|
||
| p = 0 | ||
| interval = b - a | ||
| fa = FUNC(a) | ||
| fb = FUNC(b) | ||
|
|
||
| Console.WriteLine(New String("-", 97)) | ||
| Console.WriteLine("{0,3} {1,10} {2,12} {3,12} {4,12} {5,12} {6,12} {7,12}", "p", "a", "b", "f(a)", "f(b)", "xm", "f(xm)", " interval size") | ||
| Console.WriteLine(New String("-", 97)) | ||
|
|
||
| Do | ||
| p += 1 ' **************** Start REPEAT-UNTIL loop ******************* | ||
| xm = 0.50 * (a + b) | ||
| fm = FUNC(xm) | ||
| Console.WriteLine("{0,3:F0} {1,12:F7} {2,12:F7} {3,12:E3} {4,12:E3} {5,12:F7} {6,12:E3} {7,12:E4}", p, a, b, fa, fb, xm, fm, interval) | ||
| If fa * fm > 0.0 Then | ||
| a = xm | ||
| fa = fm | ||
| Else ' case of fa*fm<0.0D0 | ||
| b = xm | ||
| fb = fm | ||
| End If | ||
| interval = 0.50 * interval | ||
| If ((Math.Abs(fm) < eps) And (interval < eps)) Or p = maxit Then Exit Do | ||
| Loop ' End the iteration loop | ||
|
|
||
| root = xm | ||
| Halves = p | ||
| If p = maxit Then | ||
| Console.WriteLine(New String("!", 37)) | ||
| Console.WriteLine("Max iteration number reached={0}", p) | ||
| Console.WriteLine(New String("!", 37)) | ||
| End If | ||
| End Sub | ||
|
|
||
| Public Function FUNC(ByVal x As Double) As Double | ||
| ' ======================================================================= | ||
| ' User-defined Function providing f(x) which should be cast as f(x)=0. | ||
| ' ======================================================================= | ||
| Return x * x + 0.025 * x - 4.0 | ||
| End Function | ||
| End Module |
Binary file not shown.