{   prog6a.pas -- Solve First Order ODE by RK2 Method
    Written Apr 19, 2001 by Eric Olson for Mathematics 483

    For information see Section 4.4 in Numerical Analysis for Applied
    Mathematics, Science, and Engineering, by Greenspan and Casulli }

Program main;

function Fc(x,y:real):real;
begin
    Fc:=y*sin(x)
end;

function Yc(x:real):real;
begin
    Yc:=exp(1.0-cos(x))
end;

function RK2(x0,y,xn:real;n:integer):real;
    var h,x,K0,K1:real;
        i:integer;
begin
    h:=(xn-x0)/n;
    for i:=1 to n do begin
        x:=x0+i*h;
        K0:=h*Fc(x,y);
        K1:=h*Fc(x+h,y+K0);
        y:=y+0.5*(K0+K1)
    end;
    RK2:=y
end;

var Ycn,yn,E:real;
    i,n:integer;
begin
    Ycn:=Yc(10.0);
    writeln('#    n    yn    err');
    n:=16;
    for i:=4 to 20 do begin
        yn:=RK2(0.0,1.0,10.0,n);
        E:=abs(yn-Ycn);
        writeln(n,yn,E);
        n:=n*2
    end
end.