Technological University of the Philippines
Taguig Campus
LABORATORY
IN
NUMERICAL METHOD
Submitted by:
BSECE2A
Balderama, Jannica
Honrado, Jasper
Rey, Ann Jessiere
Ruiz, Muel Fred
Turallo, Mira Shaine
Vierneza, Kenneth
Submitted to:
Engr. Marcelo V. Rivera
Date: March 25, 2017
BISECTION METHOD
Script:
syms x; for ctr = ctr : -1 : 2
prompt = 'Please input a function: '; iteration = iteration + 1
f(x) = input (prompt); if ((f(XL))*(f(XM))) < 0
prompt = 'Please input a value of XL: '; XL = XL
XL = input (prompt); XU = XM
prompt = 'Please input a value for XU: '; XM1 = (XL + XU)/2;
XU = input (prompt); XMN = vpa(XM1, 6)
prompt = 'Please input the number of ARTE = (abs((XM1 - XM)/XM1))*100;
iterations to be used: '; ARTE = vpa(ARTE, 4);
ctr = input (prompt); s = char (ARTE);
chk = 0; ARTE = [s, ' %']
for chk = chk : 1 : 10 XM = XM1;
if ((f(XL))*(f(XU))) < 0 elseif ((f(XL))*(f(XM))) > 0
chk = 10; XL = XM
elseif ((f(XL))*(f(XU))) > 0 XU = XU
disp ('Please input a new value for XL XM1 = (XL + XU)/2;
and XU') XMN = vpa (XM1, 6)
prompt = 'Please input a value of XL: '; ARTE = (abs ((XM1 - XM)/XM1))*100;
XL = input (prompt); ARTE = vpa (ARTE, 4);
prompt = 'Please input a value for XU: s = char (ARTE);
'; ARTE = [s, ' %']
XU = input (prompt); XM = XM1;
end else
end ctr = 1
iteration = 0; end
XM = (XL + XU)/2 end
Sample:
Please input a function: (x^3)- XU = 0.1100
(0.165*x^2)+3.993*(10^-4) XMN = 0.0825
Please input a value of XL: 0 ARTE = 33.33 %
Please input a value for XU: 0.11 iteration = 2
Please input the number of iterations to be XL = 0.0550
used: 3 XU = 0.0825
XM = 0.0550 XMN = 0.06875
iteration = 1 ARTE =20.0 %
XL = 0.0550
GAUSSIAN ELIMINATION
Script:
clc ; a(i,:)=a(i,:)-a(j,:)*(a(i,j)/a(j, j));
%input end
disp 'Gaussian Elimination Method' end
a = [25 5 1 106.8 x=zeros(1 , m);
64 8 1 177.2 for s=m:-1:1
144 12 1 279.2]; c=0;
[m,n]=size(a); for k=2:m
for j=1:m-1 c=c+a(s,k)*x(k);
for z=2:m end
if a(j, j)==0 x(s)=(a(s,n)-c)/a(s,s);
t=a(j,:);a(j,:)=a(z,:); end
a(z,i)=t; disp('Gauss elimination method ;')
end a
end x'
for i=j+1:m
Sample:
Gaussian Elimination Method
Gauss elimination method ;
a=
25.0000 5.0000 1.0000 106.8000
0 -4.8000 -1.5600 -96.2080
0 0 0.7000 0.7600
ans =
0.2905
19.6905
1.0857
GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING
Script:
a=[0.25 -1.32 3 20 b(i,:)=b(i,:)-b(j,:)*(b(i,j)/b(j,j));
1.39 2.71 9.63 34 end
0.41 2.24 -11 5]; end
%Gaussian Elimination With Partial Pivoting x=zeros(1,m);
disp(a) ; for s=m:-1:1
b = sortrows(a, -1) c=0;
%disp (b) ; for k=2:m
[m,n]=size (b) ; c=c+b(s,k)*x(k);
for j=1 :m-1 end
for z=2:m x(s) = (b(s,n)-c)/b(s,s);
if b(j,j)==0 end
t=b(j,:);b(j,:)=b(z,:); disp('Gauss Eliminaton Method With Partial
b(z,i)=t; Pivoting:');
end b
end x'
for i=j+1:m
Sample:
Gauss Eliminaton Method With Partial
0.2500 -1.3200 3.0000 20.0000 Pivoting:
1.3900 2.7100 9.6300 34.0000
0.4100 2.2400 -11.0000 5.0000 b=
1.3900 2.7100 9.6300 34.0000
b= 0 1.4406 -13.8405 -5.0288
0 0.0000 -16.0961 7.5759
1.3900 2.7100 9.6300 34.0000
0.4100 2.2400 -11.0000 5.0000
0.2500 -1.3200 3.0000 20.0000 ans =
43.3425
-8.0124
-0.4707
NEWTON RHAPSON
Script:
prompt='What is the function?'; vpa (TV , 10)
syms x ; prompt = 'How many iterations?';
f(x) = input(prompt); m = input(prompt);
numberofiteration = m
prompt = 'What is the value of x?';
syms y; for numberofiteration = 1: +1 : m
y=input(prompt); numberofiteration
Upper=f(y); TX = f(y)
vpa(TX, 10) TV = diff (f) ;
TV = diff(f); Lower = TV (y)
TV (y); y = y - (TX/TZ)
disp('first derivative is:') vpa (y , 10)
TV (y) ; end
Sample:
What is the function?: (x^3)+(4*x^2)-(10) Upper = 199283/29791
What is the value of x?2.5 Lower = 21571/961
ans = 30.625 y = 943980/668701
ans = 1.411662312
first derivative is:
numberofiteration = 3
ans(x) = 3.0*x^2 + 8.0*x
Upper =
How many iterations?3
234521792946912590/299017026184076101
numberofiteration = 3
Lower =
numberofiteration = 1
7723217681040/447161027401
Upper = 245/8
Upper =
Lower = 155/4
705604123360122661/516452338652912904
y = 53/31
ans =
ans = 1.709677419 1.36625216
numberofiteration = 2
