) 中图学技术大荸学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS f(x)≈L2(x0) 2h (-3f(x)+4f(x1)-f(x2)+,f"(5) f(x)≈L2(x1)=1(-f(x)+f(x2)-f"() f(x)≈L2(x2)=(f(x)-4f(x)+3f(x2)+,f"( f"(x)≈L2(x)=2(f(x)-2f(x)+f(x2)+[-"(5)+() f"(x)≈L"(x2)=(f(x)-2f(x)+f(x2),f((5) f"(x2)≈L"(x2)=2(f(x)-2f(x)+f(x2)+[f"(5)-f((52) Taylor)展开分析,可以知道,它们都是O(h2)称为三点公式数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS ( ) 2 0 2 0 0 1 2 1 '( ) ' ( ) 3 ( ) 4 ( ) ( ) '''( ) 2 3 h f x L x f x f x f x f h  = − + − +  ( ) 2 1 2 1 0 2 1 '( ) ' ( ) ( ) ( ) '''( ) 2 6 h f x L x f x f x f h  = − + −  ( ) 2 2 2 2 0 1 2 1 '( ) ' ( ) ( ) 4 ( ) 3 ( ) '''( ) 2 3 h f x L x f x f x f x f h  = − + +  Taylor展开分析，可以知道，它们都是 ( ) 2 O h 称为三点公式 ( ) 2 (4) 0 2 0 0 1 2 1 2 2 1 ''( ) '' ( ) ( ) 2 ( ) ( ) [ '''( ) ( )] 6 h f x L x f x f x f x hf f h  = − + + − +   ( ) 2 (4) 1 1 2 0 1 2 2 1 ''( ) '' ( ) ( ) 2 ( ) ( ) ( ) 12 h f x L x f x f x f x f h  = − + −  ( ) 2 (4) 2 2 2 0 1 2 1 2 2 1 ''( ) '' ( ) ( ) 2 ( ) ( ) [ '''( ) ( )] 6 h f x L x f x f x f x hf f h  = − + + −  