Integrare Numerica - Schema Program

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Integrare numerica Integrare numerica a functiilor a functiilor Scheme logice Scheme logice + + programe MATLAB programe MATLAB

description

Suport curs metode numerice UPB

Transcript of Integrare Numerica - Schema Program

  • 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

    ( ) ( )12)()(2)(

    1

    11

    1

    ++

    =

    =

    n

    xfxfxfxxI

    n

    n

    ii

    nmt

  • 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