how to create barcode in asp.net c# FIGURE I24 MATIAB Mljleto implement Newton Rophson method noniineor for syslemsequoiions of in Software

Drawing QR Code ISO/IEC18004 in Software FIGURE I24 MATIAB Mljleto implement Newton Rophson method noniineor for syslemsequoiions of

FIGURE I24 MATIAB Mljleto implement Newton Rophson method noniineor for syslemsequoiions of
Draw QR Code In None
Using Barcode creator for Software Control to generate, create QR-Code image in Software applications.
QR Code Recognizer In None
Using Barcode reader for Software Control to read, scan read, scan image in Software applications.
than Newton-Raphson which have betterconvergence but behaviorhave beendeveloped One approachis to refbrrrruiate nonlinearsysteul a singlefunction: the as
QR-Code Maker In C#.NET
Using Barcode printer for .NET framework Control to generate, create QR Code JIS X 0510 image in .NET framework applications.
Drawing QR Code In VS .NET
Using Barcode printer for ASP.NET Control to generate, create QR Code 2d barcode image in ASP.NET applications.
_L F(x) _\;-l
QR Encoder In Visual Studio .NET
Using Barcode encoder for .NET framework Control to generate, create QR Code JIS X 0510 image in .NET applications.
Denso QR Bar Code Maker In VB.NET
Using Barcode drawer for .NET Control to generate, create QR Code 2d barcode image in Visual Studio .NET applications.
l f i G t , x z , i r , , ) 1 2
Paint Universal Product Code Version A In None
Using Barcode creator for Software Control to generate, create UCC - 12 image in Software applications.
Drawing Code 3 Of 9 In None
Using Barcode maker for Software Control to generate, create USS Code 39 image in Software applications.
whereI (x1,,{2,,r,,) is the ith rnember the originalsystem Eq (127) values of of The of r that nlinimize this ftrnctionalso reprcserlt solutionof the nonlinearsystem the Thfle fore, nonlinearoptimizationtechniques be employedto obtain solutions can
Make Barcode In None
Using Barcode generator for Software Control to generate, create bar code image in Software applications.
Creating DataMatrix In None
Using Barcode generator for Software Control to generate, create Data Matrix image in Software applications.
I23 CASE STUDY
Painting Code 128 Code Set B In None
Using Barcode printer for Software Control to generate, create Code 128 image in Software applications.
Painting UCC-128 In None
Using Barcode printer for Software Control to generate, create EAN / UCC - 14 image in Software applications.
CHEMICAL REACTIONS
Making RoyalMail4SCC In None
Using Barcode maker for Software Control to generate, create British Royal Mail 4-State Customer Barcode image in Software applications.
USS-128 Maker In Java
Using Barcode generation for Java Control to generate, create GS1 128 image in Java applications.
Bockground' Nonlinearsystems equations of occur frequentlyin the characterization of chemicalreactions For example,the following chemicalreactions takeplacein a closed sysrem:
Bar Code Generator In Visual Studio .NET
Using Barcode encoder for ASP.NET Control to generate, create bar code image in ASP.NET applications.
Encode EAN13 In .NET
Using Barcode generation for Visual Studio .NET Control to generate, create EAN-13 image in .NET applications.
2 A+ B
UCC - 12 Drawer In None
Using Barcode generator for Office Excel Control to generate, create GS1-128 image in Office Excel applications.
Recognizing Code 3/9 In VB.NET
Using Barcode reader for .NET Control to read, scan read, scan image in .NET applications.
--->
Read Bar Code In Java
Using Barcode Control SDK for BIRT reports Control to generate, create, read, scan barcode image in BIRT applications.
Make Bar Code In None
Using Barcode drawer for Font Control to generate, create bar code image in Font applications.
(12r8) (1219)
A+D*c
At equilibrium,theycanbe characterized by Kl :3cicu Kz- 3cac,t
(1220) (122t\
where the nomenclatureci representsthe concentration of constituent i If x, and x" are the number of molesof C that are produceddue to the first and second reactions, respectively, formulatethe equilibrium,relationships a pair as of two simultaneous nonlinearequations tt : 4_x K, = 3:7x lo-2, : 50, c6s 20,c,,o: 5, and cr,6: 10, employ the ll !o-4, coo: Newton-Raphson methodto solve theie equations
Sofution Usingrhe stoichiometry Eqs(t2lg) of and(1219),the concenrrations of eachconstituent be represented termsof -r, can in and_r,as
ca:cuo-2x1 cb:cb,\-xI cc=cc,o*-tt*rz Cd=Cd,\-Xz 12
(r222) (1223) (1224)
(r225) where the subscript0 designates initial concentration the ofeach constituent Thesevalues can be substiruted inro Eqs (1220) and, (1221)ro sive
(c0*xL+x2) (coo- 2x1 - x)2{c6,0 - xr)
(c",0+xr*xz) * (c",0 2x1- x2)@a,ox:) *
Given the parametervalues,theseare two nonlinear equationswith two unknownsThus, the solution to this problem involves determining the roots of f1@1,x) f 2 @ 1 ,x 2 ):
5*xr+xz (50-2xr-x)2(20-x) (50-2xt-x)(10-xz)
-4x10-a - 37 x 10-2
(1226) (1221)
iiir";illr ir1
ITERATIVE METHODS
,''
continued
In order to use Newton-Raphson,we must determinethe Jacobianby taking thepartial derivativesof Eqs (1226) and (1227)Although this is certainly possible, evaluating the derivativesis time consuming alternative to represent An is them by finite diff'erences inr fashionsinilar to the approach usedlbr the modified secantmethodin Sec63Forexanple, the partial derivativescomprisingthe Jacobian can be evaluated as
x2) fi(xt + 6x1, * fi(xr, xz) 3xr x2) fz(xr + Er1, - ft(xt,rz) 6xr
ofr -: 3xz
3fz oxz
fi(xr,xz * 6x2) J\$r, xz) 3uz fz(xt, xz + d,r2) fz\r, xz) 3x,
3fz orr
These relationships can then be expressedas an M-file to compute both the function valuesand the Jacobianas
f unction lJ,lr =jf r-c;rct{x, varrrgin) del=0000001; c l f l d x l - ( r r( x ( I ) + c l e l * x ( I ) , x (2) )-rr (x (1) x (2 )) dfldx2= (r (x(1) ,x(2) +del"x(2) ) -u(x(1 ) ,x(2) ) c l f 2 d x 1 = ( ( x( 1 ) + d e l * x ( l - ) , x ( 2 ) ) - u ( x ( 1 ) , x ( 2 ) ) ( ' d f 2 c 1 : : 2 =r ( x ( L ) , x ( 2 ) + d e l * x ( 2 ) ) - v ( x ( f ) , x ( 2 ) ) J=fclf1dx1 df Ldx2;df2cixi df2rlx ,; 1 f 1=u(x(1),x{lt)); f2='1(x(1),x(l));
a-f f 1f t f unct ion f =u (x, !') (5 + x + y) f ,/ funct ion f-v (x, y ) f = (i + x + ,') I
t2t (^)
) ,' (de1*x t 1) ) ; ) / (del*x(2)); ) ,r(rlel*x(1,)); ) / (ciel*x(2));
system ul
T O I t-o
(b) Rep 122 Us< system u x) - 00004; a a : , - i:
,a x x
-'!)
| 0-r1 -3xt
':<,/)
(1Ll -71
The function nevrtmul t (Fig 124)can thenbe employedto determine rootsgiven the inis t i a l g u e s s eo f x , : x z : 3 :
--> forii-ai, shorL e
123 Re1 124 Tht termine( reactors reactor(1
33,r66c+000 2a,-f 2l+000 f= -'l I2B5e-017 85 7-r ,-01'1
Solve tl E s: 5 V o 125 Ust and (b) v tem to a equation
a223 7e 010 i Ler = 4
PROBLEMS
continued
a is These values After four iterations, solution x, - 33366 x, : 26772 obtained of &Dd (1225) compute equilibrium into through to the concanthenbe substituted Eq (1222) of centrations thefourconstituents: : ca : 50 - 2(33366) 26772 406496 : cn:20 - 33366 166634 cc : 5 + 33366 26112: 110138 + :73228 : lO - 26772 ca
Copyright © OnBarcode.com . All rights reserved.