Code matlab bài tập lớn Phương pháp tính thầy Nguyễn Hồng Lộc

ĐỀ PHƯƠNG PHÁP TÍNH THẦY LỘC.

Trang 1

ĐỀ PHƯƠNG PHÁP TÍNH THẦY LỘC

Trang 3

CODE BÀI TẬP LỚN PHƯƠNG PHÁP TÍNH THẦY LỘC

CÂU 1:

function Cau1

clc;

format short

syms x

mn = input('Nhap 2 so cuoi MSSV: ');

M = (mn+12)/10;

%%%%%%%%%%%%%%

f = exp(x)+2*x^2+sin(x)/M-10;

a = 1;

b = 2;

if double(subs(f,x,a)*subs(diff(diff(f,x),x),x,a))>0

X = a;

else

X = b;

end

if double(subs(diff(f,x),x,a))<double(subs(diff(f,x),x,b));

min = subs(diff(f,x),x,a);

else

min = subs(diff(f,x),x,b);

end

for i = 1:2 %chay nghiem tu x1 -> x2

X = X - subs(f,x,X)/subs(diff(f,x),x,X);

Denta = ceil((abs(subs(f,x,X))*10^4)/min)/10^4;

i = i+1;

end

x2 = double(X), SaiSo = double(Denta),

end

CÂU 2:

function Cau2

clc

format short

syms x

M = (mn+12)/10;

%%%%%%%%%%%%%%%%%%%%

A=[6+M 2 -3 4 5; 4 7+M 4 -2 -6; 3 -3 8+M -2 -5; 2 -3 4 9+M -3; 5 -3 4 -2 10+M];

B=[9;8;7;6;5];

[L , U]= lu(A);

X= inv(A)*B;

l43 = L(4,3);

u55 = U(5,5);

x5 = X(5,1);

Trang 4

a = 'Phan tu L43 la:';

disp(a);

disp (l43);

b = 'Phan tu U55 la:'; disp(b); disp(u55);

c = 'Gia tri x5 la:';

disp(c); disp (x5)

end

CÂU 3:

function Jacobi

clc;

M = (mn + 12)/10;

%%%%%%%%%%%%%%%%%%%%%%%%

a = [12+M 2 -3 4 5; 4 13+M 4 -2 -6; 3 -3 14+M 2 -5; 2 -2 4 15+M -3; 5 -4 5 -3 16+M];

b = [9; 8; 7; 6; 5];

x = [1.5; 0.3; 3.4; 1.4; 5.6];

i=0;A=x(1);B=x(2);C=x(3);D=x(4);E=x(5);

while i<3 %tim nghiem x3

X=(b(1)-a(1,2)*B-a(1,3)*C-a(1,4)*D-a(1,5)*E)/a(1,1);

Y=(b(2)-a(2,1)*A-a(2,3)*C-a(2,4)*D-a(2,5)*E)/a(2,2);

Z=(b(3)-a(3,1)*A-a(3,2)*B-a(3,4)*D-a(3,5)*E)/a(3,3);

T=(b(4)-a(4,1)*A-a(4,2)*B-a(4,3)*C-a(4,5)*E)/a(4,4);

K=(b(5)-a(5,1)*A-a(5,2)*B-a(5,3)*C-a(5,4)*D)/a(5,5);

A = X; B = Y; C = Z; D = T; E = K;

i=i+1;

end

x1 = A, x2 = B, x3 = C, x4 = D, x5 = E,

end

CÂU 4:

function GaussSeidel

clc;

M = (mn + 12)/10;

a = [12+M 2 -3 4 5; 4 13+M 4 -2 -6; 3 -3 14+M 2 -5; 2 -2 4 15+M -3; 5 -4 5 -3 17+M];

b = [9; 8; 7; 6; 4];

x = [0.1; 0.3; 0.4; 0.5; 0.9];

i=0;A=x(1);B=x(2);C=x(3);D=x(4);E=x(5);

while i<3 %tim nghiem x3

A=(b(1)-a(1,2)*B-a(1,3)*C-a(1,4)*D-a(1,5)*E)/a(1,1);

B=(b(2)-a(2,1)*A-a(2,3)*C-a(2,4)*D-a(2,5)*E)/a(2,2);

C=(b(3)-a(3,1)*A-a(3,2)*B-a(3,4)*D-a(3,5)*E)/a(3,3);

D=(b(4)-a(4,1)*A-a(4,2)*B-a(4,3)*C-a(4,5)*E)/a(4,4);

E=(b(5)-a(5,1)*A-a(5,2)*B-a(5,3)*C-a(5,4)*D)/a(5,5);

i=i+1;

Trang 5

end

x1 = A, x2 = B, x3 = C, x4 = D, x5 = E,

end

CÂU 5:

function Cau5

clc;

format short

M = (mn+12)/10;

%%%%%%%%%%%%%%%

syms x

X = [1.3 1.7 2.3 2.7 2.9 3.1];

Y = [1.2 8.6 2.3 2.5 2*M 6.6];

n = size(X,2); h=[]; b=[];d=[];

A = zeros(n);

B = zeros(n,1);

A(1,1)=1; A(n,n)=1;

for i=1:n-1

h(i) = X(i+1)-X(i);

end

for i=2:n-1

A(i,i)=2*(h(i-1)+h(i));

A(i,i-1)=h(i-1);

A(i,i+1)=h(i);

B(i,1)=3*(Y(i+1)-Y(i))/h(i)-3*(Y(i)-Y(i-1))/h(i-1); end

c = inv(A)*B;

for i=1:n-1

b(i)=(Y(i+1)-Y(i))/h(i)-h(i)*(c(i+1)+2*c(i))/3; d(i)=(c(i+1)-c(i))/(3*h(i));

end

t = 1.4;

I = 0;

for i =1:n-1

if t>= X(i) && t<X(i+1)

I = Y(i) + b(i)*(t-X(i)) + c(i)*(t-X(i))^2 + d(i)*(t-X(i))^3; end

end

fprintf('Xap xi gia tri cua ham tai x = %.1f',t);

disp(I);

t = 2.5;

I = 0;

for i =1:n-1

if t>= X(i) && t<X(i+1)

Trang 6

I = Y(i) + b(i)*(t-X(i)) + c(i)*(t-X(i))^2 + d(i)*(t-X(i))^3; end

end

disp(I);

end

CÂU 6:

function Cau6

clc;

format short ;

syms x m real

M = (mn+12)/10;

X = [1.3 1.7 2.3 2.7 2.9 3.1];

Y = [1.2 8.6 2.3 2.5 3*M 6.6];

n = size(X,2);

g1 = 0.2;

gn = 0.5;

for i = 1:n-1

H(i) = X(i+1) - X(i);

end

A(1) = 2*H(1);

A(n) = 2*H(n-1);

for j = 2:n-1

A(j) = 2*(H(j-1) + H(j));

end

B(1) = 3*(Y(2)-Y(1))/H(1)-3*g1;

B(n) = 3*gn - 3*(Y(n)-Y(n-1))/H(n-1);

for k = 2:(n-1)

B(k) = 3*(Y(k+1)-Y(k))/H(k) - 3*(Y(k)-Y(k-1))/H(k-1); end

D = diag(A,0); E = diag(H,1); F = diag(H,-1);

C = inv(E+F+D)*(B');

for l = 1:(n-1)

d(l) = (C(l+1)-C(l))/(3*H(l));

b(l) = (Y(l+1)- Y(l))/H(l) - H(l)*(C(l+1)+2*C(l))/3; end

t = 1.4;

I = 0;

for i =1:n-1

if t>= X(i) && t<X(i+1)

I = Y(i) + b(i)*(t-X(i)) + C(i)*(t-X(i))^2 + d(i)*(t-X(i))^3; end

end

Trang 7

disp(I);

t = 3.0;

I = 0;

for i =1:n-1

if t>= X(i) && t<X(i+1)

I = Y(i) + b(i)*(t-X(i)) + C(i)*(t-X(i))^2 + d(i)*(t-X(i))^3; end

end

disp(I);

end

CÂU 7:

function Cau7

clc;

format short

syms x m

M = input('Nhap M: ');

%%%%%%%%%%%%%%%%%%%%

u = [1.2 1.3 1.4 1.5 1.7];

y = [2*M 2.5 5 4.5 5.5];

gx = sqrt(x.^2+1);

hx = cos(x);

A = zeros(2); B = zeros(2,1);

for i = 1:5

A(1,1)=A(1,1)+subs(gx.^2,u(i)) ;

A(2,2)=A(2,2)+subs(hx.^2,u(i));

A(1,2)=A(1,2)+subs(hx.*gx,u(i));

B(1,1)=B(1,1)+y(i)*subs(gx,u(i));

B(2,1)=B(2,1)+y(i)*subs(hx,u(i));

end

A(2,1) = A(1,2);

C = inv(A)*B;

A = C(1), B = C(2),

end

CÂU 8:

function Cau8

clc;

M = (mn+12)/10;

syms x

%%%%%%%%%%%%%%%%%

p = [0.1 0.3 0.6 0.9 1.1 1.4];

Trang 8

q = [3*M 0.6 1.5 3.7 3.2 4.3];

x1 = 1; x2 = 1; x3 = 1; x4 =1; x5 = 1;

for i = 1:(size(p,2)-1)

a(i) = (q(i+1)-q(i))/(p(i+1)-p(i));

x1 = x1*(x-p(i));

end

for i = 1:(size(a,2)-1)

b(i) = (a(i+1)-a(i))/(p(i+2)-p(i));

x2 = x2*(x-p(i));

end

for i = 1:(size(b,2)-1)

c(i) = (b(i+1)-b(i))/(p(i+3)-p(i));

x3 = x3*(x-p(i));

end

for i = 1:(size(c,2)-1)

d(i) = (c(i+1)-c(i))/(p(i+4)-p(i));

x4 = x4*(x-p(i));

end

for i = 1:(size(d,2)-1)

e(i) = (d(i+1)-d(i))/(p(i+5)-p(i));

x5 = x5*(x-p(i));

end

A = subs(diff((q(1)+a(1)*x5+b(1)*x4+c(1)*x3+d(1)*x2+e(1)*x1),x),x,0.5); disp('gia tri xap xi dao ham cap 1 cua ham tai x=0.5 la:');disp(double(A)); end

CÂU 9:

function Cau9

clc;

syms x y;

M = (mn+12)/10;

%%%%%%%%%%%%%%%%

a= 2;

b = 62;

n =120;

h= (b-a)/n;

m=n/2;

f= (2*M*x^2+x+1)/(7*x^4+x+6);

y= subs(f,x,a)+subs(f,x,b)+4*subs(f,x,a+h);

for i = 1 :m-1

y= y+ 2*subs(f,x,a+2*i*h)+4*subs(f,x,a+(2*i+1)*h);

end

y=double(y*h/3);

disp(y);

Trang 9

end

CÂU 10:

function Cau10

format short;

clear all;

clc;

syms x u y;

M = (mn+12)/10;

h = 0.2;

x1 = 1;

y1 = 2.4;

xi = 2.2;

f = 2*M.*x+x.*sin(x+2.*y);

K1 = 0; K2 = 0; K3 = 0; K4 = 0;

u = [];u(1) = x1;

k = (xi-x1)/h;

for i=1:k

u(i+1)= u(i) + h;

end

y = []; y(1) = y1;

for i=1:round(k)

K1=h*subs(subs(f,u(i)),y(i));

K2=h*subs(subs(f,u(i)+h/2),y(i)+K1/2); K3=h*subs(subs(f,u(i)+h/2),y(i)+K2/2); K4=h*subs(subs(f,u(i)+h),y(i)+K3); y(i+1)=y(i)+(K1+2*K2+2*K3+K4)/6; end

n = round(k+1);

disp('Xap xi: '), y(n),

end

CÂU 11:

function Cau11

clc;

format short

syms x real

M = (mn+12)/10;

a = 0; b = 1;

h = 0.1; ya = 1; yb = 1.2;

n = (b-a)/h;

px = x + 2*M;

qx = x.^3;

rx = -30;

Trang 10

fx = -x.*(x+1);

for i = 1:n

x(i) = a + i*h;

end

n = round(n);

A = zeros(n-1);

B = zeros(n-1,1);

A(1,1) = subs(rx,x(1)) - 2*subs(px,(x(1)))/(h^2);

A(1,2) = subs(px,x(1))/(h^2) + subs(qx,x(1))/(2*h);

A(n-1,n-1) = subs(rx,x(n-1)) - 2*subs(px,x(n-1))/(h^2);

A(n-1,n-2) = subs(px,x(n-1))/(h^2) - subs(qx,x(n-1))/(2*h); B(1,1) = subs(fx,x(1)) - subs((px/(h^2)-qx/(2*h)),x(1))*ya; B(n-1,1) = subs(fx,x(n-1))-subs((px/(h^2)+qx/(2*h)),x(n-1))*yb; for i=2:n-2

A(i,i) = subs(rx,x(i)) - 2*subs(px,(x(i)))/(h^2);

A(i,i-1) = subs(px,x(i))/(h^2) - subs(qx,x(i))/(2*h);

A(i,i+1) = subs(px,x(i))/(h^2) + subs(qx,x(i))/(2*h);

B(i,1) = subs(fx,x(i));

end

C = inv(A)*B;

Xap = 'Xap xi gia tri cua ham y(0.1) = ';disp(Xap);disp(C(1)); Xap = 'Xap xi gia tri cua ham y(0.5) = ';disp(Xap);disp(C(5)); Xap = 'Xap xi gia tri cua ham y(0.9) = ';disp(Xap);disp(C(9)); end

Định dạng
Số trang	10
Dung lượng	373,67 KB