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EEE 212: Numerical Technique Laboratory

No. of Experiment : 5

Name of Experiment : Solution of Simultaneous Linear Algebric

Equations

Date of Performance: 23-05-2012

Date of Submission: 30-05-2012

Tahmid Sami Rahman

0906016

Department: EEE

Section: A

Md. Ayaz Masud

0906021

Department: EEE

Section: A

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Problem

Solve the boundary value problem for

= 1.2510 where h=1

Plot the solution using

i) PINVii) Gauss Seidel Method (error

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Graph

PINV:

Elapsed time is 0.047521 seconds.

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Gauss Elimination with Pivoting:

Elapsed time is 0.444923 seconds.

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Gauss Seidel Method:

Elapsed time is 3.965348 seconds.

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Combined Graph:

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Appendix

Code for the Solution

cl ear al l ; h=10 - 6; A=zer os( 100, 100) ; A( 1, 1)=1; A( 101, 101) =1; f or i =2: 100

j =i ; A( i , j - 1) =1; A( i , j ) =- 2;

A( i , j +1) =1;

endx=0: h: 10 - 4; B=zeros( 1, 101) ; B( 1, 1)=5; B( 1, 101)=0;

f or i =2: 101B( i ) =1. 25. *10 12. *exp( - 5. *10 5. *x( i ) ) . *( h 2) ; endt i ce=pi nv( A) *B' ; t oc

di sp( e) ;

% pl ot ( d, ' r ' ) ; % hol d on;

pl ot ( e, ' b' ) ; hol d on;

a=A; b=B;

aj i =0;

t i cs=si ze( a) ; f or i =1: s(1) - 1

f or j =i +1: s( 1) aj i =a( j , i ) ;

f or k=1: s( 2) a( j , k) =a( j , k) - ( aj i . / a( i , i ) ) . *a( i , k) ;

end

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b( j ) =b( j ) - ( aj i . / a( i , i ) ) . *b( i ) ; end

end

di sp( a) ; di sp( b) ;

x=b;

n=s( 2) ; sum=0;

x( n) =b( n) . / a( n, n) ;

f or i =n- 1: - 1: 1sum=b( i ) ;

f or j =i +1: nsum=sum- a( i , j ) . *x(j ) ;

endx( i ) =sum. / a( i , i ) ;

end

%di sp( x) ;

pl ot ( x, ' o' ) ;hol d on;

t oc%gauss sei del

t i c

x=b; h=10 - 6; i =1; f or h=0: 10 - 6: 10 - 4x(i ) =5. *exp( - 5000. *h) ; i =i +1;

end

xr ef =x;

check=0;

whi l e( 1) f or i =1: 101

sum=b( i ) ; f or j =1: 101

i f i ~=j sum=sum- ( a( i , j ) . *x( j ) ) ; end

endx( i ) =sum. / a( i , i ) ;

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end

xsol =xref - x;

f i ni sh=0;

f or i =1: 101i f xsol ( i ) >10 - 9

f i ni sh=1; end

end

i f( f i ni sh==0) break;

end

xref =x; % check=check+1; % i f check==1000% br eak; % endend

pl ot ( xref , ' g' ) ;

t oc