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Fortran 77 Programs Fortran 77 Programs Related to the Book Book Title: Author: Publisher: Publication Place: New York Publication Date: September, 1997 ISBN's: 0-521-48143-0 (hardback); 0-521-48592-4 (paperback) List Prices: $110 (hardback); $42.95 (paperback) Other Info: 393 Pages; 7 x 10; 30 Line Diagrams; 5 Tables; 94 Exercises; Bibliography and Index Please Note: • Most programs listed here have appeared in the book (as indicated), which are copyrighted by Cambridge University Press. • No warranties, express or implied, are made for any materials at this site.

Introduction •: One-dimensional motion under a harmonic force (appeared in the book). Basic Numerical Methods •: Lagrange interpolation with the Aitken method (appeared in the book). •: Lagrange interpolation with the upward/downward correction method. •: Orthogonal polynomials generator (appeared in the book). •: Millikan experiment fit (appeared in the book). •: Millikan experiment with a direct linear fit. •: Derivatives with the three-point formulas (appeared in the book).

•: Integration with the Simpson rule (appeared in the book). •: Root Search with the bisection method (appeared in the book). •: Root Search with the Newton method (appeared in the book). •: Root Search with the secant method (appeared in the book).

Cartea Tibetana A Vietii Si A Mortii Pdf here. •: Bond length of NaCl (appeared in the book). •: Classical scattering (appeared in the book). •: Uniform random number generator (appeared in the book).

•: Exponential random number generator (appeared in the book). •: Gaussian random number generator (appeared in the book). •: Two-dimensional percolation (appeared in the book).

Ordinary Differential Equations •: Simplest predictor-corrector scheme (appeared in the book). •: Pendulum solved with the fourth order Runge-Kutta algorithm (appeared in the book).

•: Boundary-value problem solved with the shooting method (appeared in the book, with minor modifications). •: Simplest algorithm for the Sturm-Liouville equation (appeared in the book). •: The Numerov algorithm from Eqs. •: The Numerov algorithm from Eqs. •: An application of Program 3.A. •: Eigenvalue problem of the 1D Schroedinger equation.

Numerical Methods for Matrices •: The partial pivoting Gaussian elimination scheme (appeared in the book). •: Determinant evaluated with the Gaussian elimination scheme (appeared in the book). •: Linear equation set solved with the Gaussian elimination scheme (appeared in the book). •: Matrix inversion with the Gaussian elimination scheme (appeared in the book). •: Determinant polynomials generator (appeared in the book). •: Random matrix generator (appeared in the book).

Spectral Analysis and Gaussian Quadrature •: Discrete Fourier transform (appeared in the book). •: Fast Fourier transform (appeared in the book). •: Power spectrum of a driven pendulum.

•: Fast Fourier transform in two dimensions (appeared in the book). •: The Legendre polynomials generator (appeared in the book). •: The Bessel functions generator (appeared in the book). Partial Differential Equations •: The bench problem (appeared in the book). •: The relaxation scheme for one dimension (appeared in the book).

•: Ground water dynamics (appeared in the book). •: The time-dependent temperature field (appeared in the book). Molecular Dynamics •: Halley's comet studied with the Verlet algorithm (appeared in the book). •: The Maxwell velocity distribution generator (appeared in the book). Modeling Continuous Systems •: A simple example on finite element method (appeared in the book).

Monte Carlo Simulations •: An example with random sampling (appeared in the book). •: An example with importance sampling (appeared in the book). High-Performance Computing •: An example of communication in MPI environment (appeared in the book). •: An MPI program on evaluation of the Euler constant (appeared in the book).

Contents • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • [ ] with Ada. Text_Io; use Ada. Text_Io; procedure Roots_Of_Function is package Real_Io is new Ada. Translation of: print_roots = (f, begin, end, step ) -># Print approximate roots of f between x=begin and x=end, # using sign changes as an indicator that a root has been # encountered. X = begin y = f (x ) last_y = y cross_x_axis = ->(last_y 0 ) or (last_y >0 and y # Smaller steps produce more accurate/precise results in general, # but for many functions we'll never get exact roots, either due # to imperfect binary representation or irrational roots.

Step = 1 / 256 f1 = (x ) ->x *x *x - 3 *x *x + 2 *x print_roots f1, - 1, 5, step f2 = (x ) ->x *x - 4 *x + 3 print_roots f2, - 1, 5, step f3 = (x ) ->x - 1.5 print_roots f3, 0, 4, step f4 = (x ) ->x *x - 2 print_roots f4, - 2, 2, step output >coffee roots.coffee ----- Root found at 0 Root found at 1 Root found at 2 ----- Root found at 1 Root found at 3 ----- Root found at 1.5 ----- Root found near -1.4140625 Root found near 1.41796875 [ ]. Output: Root found at 8.6218e-16 Root found at 1.000016 Root found at 1.998914 [ ]% Implemented by Arjun Sunel - module (roots ).

- export ( [main / 0 ] ). Main ( ) ->F = fun ( X ) ->X * X * X - 3 * X * X + 2 * X end, Step = 0.001,% Using smaller steps will provide more accurate results Start = - 1, Stop = 3, Sign = F ( Start ) >0, X = Start, while ( X, Step, Start, Stop, Sign, F ). While ( X, Step, Start, Stop, Sign, F ) ->Value = F ( X ), if Value == 0 ->% We hit a root: format ( 'Root found at ~p~n', [ X ] ), while ( X + Step, Step, Start, Stop, Value >0, F ); ( Value% We passed a root: format ( 'Root found near ~p~n', [ X ] ), while ( X + Step, Step, Start, Stop, Value >0, F ); X >Stop ->: format ( ' ); true ->while ( X + Step, Step, Start, Stop, Value >0, F ) end. Output: Root found near 8.6218e-16 Root found near 1.000016 Root found near 2.998915 ok [ ] PROGRAM ROOTS_FUNCTION!VAR E,X,STP,VALUE,S%,I%,LIMIT%,X1,X2,D FUNCTION F(X) F=X*X*X-3*X*X+2*X END FUNCTION BEGIN X=-1 STP=1.0E-6 E=1.0E-9 S%=(F(X)>0) PRINT('VERSION 1: SIMPLY STEPPING X') WHILE XLIMIT% THEN PRINT('ERROR: FUNCTION NOT CONVERGING') EXIT END IF D=(X2-X1)/(F(X2)-F(X1))*F(X2) IF ABS(D). Output: Root (to 12DP) Max. Error 0.08 1e-06 1.16 1e-06 2.34 1e-06 Note that the roots found are all near misses because fractional numbers that seem nice and 'round' in decimal (such as 10^-6) often have some rounding error when represented in binary.

To increase the chances of finding exact integer roots, try using an integer start value with a step value that is a power of two. -- Main procedure print ( 'Root (to 12DP) tMax. Error n' ) for _, r in pairs (root (f, - 1, 3, 2 ^- 10 ) ) do print ( string.format ( '%0.12f', r. Saint Seiya The Lost Canvas 1 Temporada Download Legendado here. val ), r.err ) end. Output: findRoots(#f, -1, 3, 0.0001) Root found at 0 Root found at 1 Root found at 2 findRoots(#f, -1.000001, 3, 0.0001) Root near 9.0713e-005 Root near 1.000099 Root near 2.000099 [ ] If the equation is a polynomial, we can put the coefficients in a vector and use roots: a = [ 1, - 3, 2, 0 ]; r = (a );% let's print it for = 1: 3 n = (a, r ( ) ); ( 'x%d =%f (%f',, r ( ), n ); if (n!= 0.0 ) ( ' not' ); endif ( ' exact) n' ); endfor Otherwise we can program our (simple) method.

Translation of: Procedure.d f (x.d ) ProcedureReturn x *x *x - 3 *x *x + 2 *x EndProcedure Procedure main ( ) OpenConsole ( ) Define.d StepSize = 0.001 Define.d Start =- 1, stop = 3 Define.d value =f (start ), x =start Define.i oldsign =Sign (value ) If value = 0 PrintN ( 'Root found at ' + StrF (start ) ) EndIf While x oldsign PrintN ( 'Root found near ' + StrF (x ) ) ElseIf value = 0 PrintN ( 'Root found at ' + StrF (x ) ) EndIf oldsign =Sign (value ) x +StepSize Wend EndProcedure main ( ) [ ].