第五次作業 -- 請寫出避免數值誤差的 n 次微分程式

[ccckmit]

const h = 0.001

function df(f, x, n) {
  if (n===0) return f(x)
  return (df(f,x+h,n-1)-df(f,x,n-1))/h
}

function f(x) {
  return Math.exp(x)
  // return Math.sin(x)
}

for (let n=0; n<=15; n++) {
  console.log('df(f,1,%d)=', n, df(f, 1, n))
}

執行結果

csienqu-teacher:04-search csienqu$ node diffn
df(f,1,0)= 2.718281828459045
df(f,1,1)= 2.7196414225332255
df(f,1,2)= 2.721001696848191
df(f,1,3)= 2.7223623355610016
df(f,1,4)= 2.724043213220284
df(f,1,5)= 2.220446049250313
df(f,1,6)= 1332.2676295501878
df(f,1,7)= -3108624.4689504383
df(f,1,8)= 5329070518.200751
df(f,1,9)= -5329070518200.751
df(f,1,10)= -3996802888650563.5
df(f,1,11)= 37747582837255315000
df(f,1,12)= -1.2390088954816745e+23
df(f,1,13)= 3.0908609005564358e+26
df(f,1,14)= -6.634692795159935e+29
df(f,1,15)= 1.2803091919977304e+33