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Suport curs metode numerice UPB
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Integrare numerica Integrare numerica a functiilora functiilor
Scheme logice Scheme logice ++
programe MATLABprograme MATLAB
Regula trapezelor
Schema logica
% Date intrare:xi = [ 0 0.4];yi = [ 0.2 2.4];
Transcrierea schemei in MATLAB
Irt=(xi(2)-xi(1))*(yi(2)+yi(1))/2;
%Valori finale: out=[Irt];disp(out); %valoarea obtinuta prin regula trapezului
Transpunerea in MATLAB
function [Imt] = trapezr% integrare prin regula trapezelor
% Date intrare:xi = [ 0 0.4];yi = [ 0.2 2.4];
Irt=(xi(2)-xi(1))*(yi(2)+yi(1))/2;%Valori finale: out=[Irt];disp(out); %valoarea obtinuta prin regula trapezului
end
Metoda trapezelor
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Schema logica
% Date intrare:xi = [ 0 0.4 0.8];yi = [ 0.2 2.4 4.7];n=3; %numar de puncte
Transcrierea schemei in MATLAB
S=0;for i=2:n-1
S= S+yi(i); end;
Imt=(xi(n)-xi(1))*(yi(1)+2*S+yi(n))/2/(n-1);
%Valori finale: out=[Imt];disp(out); %valoarea obtinuta prin metoda trapezului
Transpunerea in MATLAB
function [Imt] = trapezm% integrare prin metoda trapezelor
% Date intrare:xi = [ 0 0.4 0.8];yi = [ 0.2 2.4 4.7];n=3; %numar de puncteS=0;for i=2:n-1
S= S+yi(i); end;Imt=(xi(n)-xi(1))*(yi(1)+2*S+yi(n))/2/(n-1);%Valori finale: out=[Irt];disp(out); %valoarea obtinuta prin metoda trapezuluiend
Regula Simpson
Schema logica
% Date intrare:xi = [ 0 0.4 0.8];yi = [ 0.2 2.4 4.7];
Transcrierea schemei in MATLAB
Irs=(xi(3)-xi(1))*(yi(1)+4*yi(2)+yi(3))/6;
%Valori finale: out=[Irs];disp(out); %valoarea obtinuta prin regula Simpson
Transpunerea in MATLAB
function [Imt] = Simpsonr% integrare prin regula Simpson
% Date intrare:xi = [ 0 0.4 0.8];yi = [ 0.2 2.4 4.7];
Irs=(xi(3)-xi(1))*(yi(1)+4*yi(2)+yi(3))/6;%Valori finale: out=[Irs];disp(out); %valoarea obtinuta prin regula Simpsonend
Metoda Simpson
Schema logica
% Date intrare:xi = [ 0 0.2 0.4 0.6 0.8];yi = [ 0.2 1.3 2.4 3.4 4.7];
n=5; %numar de puncte; obligatoriu n=impar
Transcrierea schemei in MATLAB
Si=0;Sp=0;
% suma valori parefor i=2:2:n-1
Sp= Sp+yi(i); end;
% suma valori imparefor i=3:2:n-2
Si=Si+yi(i); end;
%Valori finale: out=[Ims];disp(out); %valoarea obtinuta prin metoda Simpson
Transpunerea in MATLABfunction [ImS] = Simpsonm% integrare prin metoda Simpson% Date intrarexi = [ 0 0.2 0.4 0.6 0.8];yi = [ 0.2 1.3 2.4 3.4 4.7]; n=5; %obligatoriu impar
Si=0;Sp=0; for i=2:2:n-1 Sp= Sp+yi(i); % suma valori pare
end;for i=3:2:n-2 Si=Si+yi(i); % suma valori impare
end; ImS=(xi(n)-xi(1))* (yi(1)+4*Sp+2*Si+yi(n))/3/(n-1);out=[ImS]; disp(out);
end