intgauss.m

数值积分的几种算法

function I = IntGauss(f,a,b,n,AK,XK)
if(n<5 && nargin == 4)
    AK = 0;
    XK = 0;
else
    XK1=((b-a)/2)*XK+((a+b)/2);
    I=((b-a)/2)*sum(AK.*subs(sym(f),findsym(f),XK1));
end

ta = (b-a)/2;
tb = (a+b)/2;
switch n
    case 0,
        I=2*ta*subs(sym(f),findsym(sym(f)),tb);
        
    case 1,
        I=ta*(subs(sym(f),findsym(sym(f)),ta*0.5773503+tb)+...
            subs(sym(f),findsym(sym(f)),-ta*0.5773503+tb));
        
    case 2,
        I=ta*(0.55555556*subs(sym(f),findsym(sym(f)),ta*0.7745967+tb)+...
            0.55555556*subs(sym(f),findsym(sym(f)),-ta*0.7745967+tb)+...
            0.88888889*subs(sym(f),findsym(sym(f)),tb));
           
    case 3,
        I=ta*(0.3478548*subs(sym(f),findsym(sym(f)),ta*0.8611363+tb)+...
            0.3478548*subs(sym(f),findsym(sym(f)),-ta*0.8611363+tb)+...
            0.6521452*subs(sym(f),findsym(sym(f)),ta*0.3398810+tb)...
            +0.6521452*subs(sym(f),findsym(sym(f)),-ta*0.3398810+tb));
  
        
    case 4,
        I=ta*(0.2369269*subs(sym(f),findsym(sym(f)),ta*0.9061793+tb)+...
            0.2369269*subs(sym(f),findsym(sym(f)),-ta*0.9061793+tb)+...
            0.4786287*subs(sym(f),findsym(sym(f)),ta*0.5384693+tb)...
            +0.4786287*subs(sym(f),findsym(sym(f)),-ta*0.5384693+tb)+...
            0.5688889*subs(sym(f),findsym(sym(f)),tb));
end