all

all other

newton raphson

clc

clear

g = @(x) cos(x) - x*exp(x);

dg = @(x) -sin(x) - exp(x) - x*exp(x);

x0 = 1;

error_nr = 10^(-4);

while true

x1 = x0 - g(x0)/dg(x0);

if abs(x1-x0) < error_nr

break

end

x0 = x1;

end

fprintf('Root = %f\n',x1);

SECANT

clc

clear

f = @(x) cos(x) - x.*exp(x);

x0 = 0;

x1 = 1;

error = 10^(-4);

while abs(x1-x0) > error

x2 = x1 - f(x1)*(x1-x0)/(f(x1)-f(x0));

x0 = x1;

x1 = x2;

end

root_secant = x1

FIXED POINT

clear

clc

f = @(x) cos(x) - x.*exp(x);

g = @(x) cos(x)./exp(x);

x0 = 0.5;

error = 10^(-4);

while true

x1 = g(x0);

if abs(x1-x0) < error

break

end

x0 = x1;

end

root_fixed_point = x1

REGULAR FALSI clear

clc

h = @(x) cos(x) - x.*exp(x);

c = 0;

d = 1;

error = 10^(-4);

while true

x = (c*h(d) - d*h(c)) / (h(d)-h(c));

if abs(h(x)) < error

break

end

if h(c)*h(x) < 0

d = x;

else

c = x;

end

end

root_regula_falsi = x

NEWTON METHOD FOR NON LINEAR

clear

clc

f1 = @(x,y) y*cos(x*y) + 1;

f2 = @(x,y) sin(x*y) + x - y;

df1dx = @(x,y) -y^2*sin(x*y);

df1dy = @(x,y) cos(x*y) - x*y*sin(x*y);

df2dx = @(x,y) y*cos(x*y) + 1;

df2dy = @(x,y) x*cos(x*y) - 1;

x = 1;

y = 2;

error = 10^(-4);

while true

F = [f1(x,y); f2(x,y)];

J = [df1dx(x,y) df1dy(x,y);

df2dx(x,y) df2dy(x,y)];

delta = inv(J)*F;

x_new = x - delta(1);

y_new = y - delta(2);

if max(abs([x_new-x , y_new-y])) < error

break

end

x = x_new;

y = y_new;

end

x_solution = x_new

y_solution = y_new