Es84 Lab Fin

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Meilyssa A. Mayormita ES84 lab

BSECE 3 BF78ATH67

CODES

Bisection Method

fprintf('\n~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~\n');

fprintf('This program will use Bisection to solve for the root of the');

fprintf('\nfunction f(x) found between xl and xu, given an error criterion.\n\n');

f = input('function : f(x) = ','s');

xl = input('lower limit of interval, xl : ');

xu = input('upper limit of interval, xu : ');

if xl>=xu

error('Input lower boundary must be less than input upper boundary.');end

errcrit = input('error criterion (in %) : ');

x=xl; fxl=eval(f);

x=xu; fxu=eval(f);

if fxl*fxu>0

error('No root exists in the given interval.');

end

if fxl==0

xr=xl; its=0; err=0;

elseif fxu==0xr=xu; its=0; err=0;

else

x=0.5*(xl+xu);

ft=eval(f);

if ft*fxl>0

xr=xl;

else

xr=xu;

end

its=0;

while (1)

xro=xr;

xr=0.5*(xl+xu);x=xl; fxl=eval(f);

x=xr; fxr=eval(f);

if (fxl*fxr>0)

xl=xr;

else

xu=xr;

end

err=100*abs((xr-xro)/xr);

if err

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Newton-Raphson Method

fprintf('\n~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~\n');

fprintf('This program will use the Newton-Raphson Method to solve for');

fprintf('\nthe root of the function f(x), without requiring an interval,');

fprintf('\ngiven an initial value xi and an error criterion to be met.\n\n');

f = input('function : f(x) = ','s');xp = input('initial value, xi : ');

errcrit = input('error criterion (in %) : ');

its=0;

while (1)

x=xp; fxp=eval(f);

x=x+1e-11; fxq=eval(f);

dfxp=(fxq-fxp)/1e-11;

xn=xp-fxp/dfxp;

xo=xp;

xp=xn;

err=100*abs((xp-xo)/xp);

its=its+1;if err=xu

error('Input lower boundary must be less than input upper boundary.');

end

p = input('number of panels , p : ');

bet=0;

d=(xu-xl)/p;

i=0;

x=xl;

while i

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Simpsons 1/3 Rule

fprintf('\n~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~\n');

fprintf('This program will use Simpson''s 1//3 Rule to solve for the');

fprintf('\nintegral of the function f(x) from xl to xu, given p panels.\n');

fprintf('Note that this can only be used when p is even.\n\n');

f = input('function : f(x) = ','s');xl = input('lower limit of integral, xl : ');

xu = input('upper limit of integral, xu : ');

if xl>=xu

error('Input lower boundary must be less than input upper boundary.');

end

p = input('number of panels , p : ');

if rem(p,2)~=0

error('Number of panels must be even.');

end

d=(xu-xl)/p;betodd=0;

i=1;

x=xl+d;

while i

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Gauss-Seidel Method

clear;

fprintf('\n\n~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-

~\n');

fprintf('This program will solve for the solution vector [x] in [A][x]=[b],');

fprintf('\ngiven the error criterion for maximum error among all variables.\n\n');n = input('size of matrix A (nxn) : n = ');

if ~(n>0)

error('n must be a positive.');

end

for i=1:n

j=1;

while j

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SAMPLE OUTPUT

Bisection Method Sample Output

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This program will use Bisection to solve for the root of the

function f(x) found between xl and xu, given an error criterion.

function : f(x) = exp(x)/(1+exp(x))-3*cos(x)+(x.^3)/11

lower limit of interval, xl : 0

upper limit of interval, xu : 5

error criterion (in %) : 1e-11

root = 1.24742

percent error = 5.6961e-012%

number of iterations = 45

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Newton-Raphson Method Sample Output

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This program will use the Newton-Raphson Method to solve for

the root of the function f(x), without requiring an interval,

given an initial value xi and an error criterion to be met.

function : f(x) = exp(x)/(1+exp(x))-3*cos(x)+(x.^3)/11initial value, xi : 0


root = 1.24742

percent error = 4.45008e-013%

number of iterations = 10

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Trapezoidal Rule Sample Output

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This program will use the Trapezoidal Rule to solve for the

integral of the function f(x) from xl to xu, given p panels.

function : f(x) = exp(x)/(1+exp(x))

lower limit of integral, xl : 0

upper limit of integral, xu : 5

number of panels , p : 1

The integral of f(x) from 0 to 5 is

3.73327

with percent error of 13.4529%.

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This program will use the Trapezoidal Rule to solve for the







4.30729


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Simpsons 1/3 Rule Sample Output

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This program will use Simpson's 1//3 Rule to solve for the


Note that this can only be used when p is even.



upper limit of integral, xu : 5number of panels , p : 2


4.3249


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This program will use Simpson's 1//3 Rule to solve for the


Note that this can only be used when p is even.






4.31357

with percent error of 1.76478e-007%.

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Gauss-Seidel Method Sample Output

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This program will solve for the solution vector [x] in [A][x]=[b],

given the error criterion for maximum error among all variables.

size of matrix A (nxn) : n = 3

a11 : 3

a12 : -0.1

a13 : -0.2

a21 : 0.1

a22 : 7

a23 : -0.3

a31 : 0.3

a32 : -0.2

a33 : 10

A =

3.0000 -0.1000 -0.2000

0.1000 7.0000 -0.3000

0.3000 -0.2000 10.0000

b1 : 7.85

b2 : -19.3

b3 : 71.4

b =

7.8500

-19.3000

71.4000


x =

3.0000

-2.5000

7.0000

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Es84 Lab Fin

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