Need help with the formula

Hi

Need help with the formula:

Code:

---

Program Simpson;
uses Crt;
const
  a=1;
  b=3;
var
  n,l:integer;
  eps,g1,g2:real;

function f(x:real):real;
 begin
  f:=x;
 end;

procedure Simp(n1:integer;var s:real);
var
  i:integer;
  h:real;
  s1,s2:real;
begin
  h:=(b-a)/n1;
  s1:=0;
  s2:=0;
  for i:=1 to n1-1 do
    if i mod 2=0 then s1:=s1+f(a+i*h)
      else s2:=s2+f(a+i*h);
  s:=h/3*(f(a)+f(b)+2*s2+4*s1);
end;{end Simp}

begin {Main}
  ClrScr;
  write('n='); readln(n);
  writeln;
  Simp(n,g1);
  eps:=-1; l:=0;
  repeat
      n:=2*n;
      Simp(n,g2);
      eps:=abs(g1-g2);
      g1:=g2;
      l:=l+1;
  until (eps<1e-3 ) or (l>100);
  if l>100 then  writeln('rozbigna')
    else begin
      writeln('g=',g2);
      writeln('n=',n);
      writeln('l=',l);
    end;
  readln;
end. {end Main}

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Quote:

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Originally Posted by terramall

Hi

Need help with the formula:

Code:

---

Program Simpson;
uses Crt;
const
  a=1;
  b=3;
var
  n,l:integer;
  eps,g1,g2:real;

function f(x:real):real;
 begin
  f:=x;
 end;

procedure Simp(n1:integer;var s:real);
var
  i:integer;
  h:real;
  s1,s2:real;
begin
  h:=(b-a)/n1;
  s1:=0;
  s2:=0;
  for i:=1 to n1-1 do
    if i mod 2=0 then s1:=s1+f(a+i*h)
      else s2:=s2+f(a+i*h);
  s:=h/3*(f(a)+f(b)+2*s2+4*s1);
end;{end Simp}

begin {Main}
  ClrScr;
  write('n='); readln(n);
  writeln;
  Simp(n,g1);
  eps:=-1; l:=0;
  repeat
      n:=2*n;
      Simp(n,g2);
      eps:=abs(g1-g2);
      g1:=g2;
      l:=l+1;
  until (eps<1e-3 ) or (l>100);
  if l>100 then  writeln('rozbigna')
    else begin
      writeln('g=',g2);
      writeln('n=',n);
      writeln('l=',l);
    end;
  readln;
end. {end Main}

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credit (formulas and codes) - @essaywriting.ninja

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If it is continuous, then when introducing the conditions for decreasing the maximum step, proportional, it can be proposed and justified by the analogue of the Runge rule of error estimation. Here m + 1 is the order of the main item of the error quadrature.