Numerical Finite Differences Solution Equations Waa=f suggests j+l 2i;+uj f(∞)1≤j≤7 0 7+1 0 A i=f SMA-HPC⊙2003MT Finite Differences 5
Numerical Finite Differences Solution Equations 2-10 f(a1) 12-1 f(a2) A △ -12-1 f(an-1 0…0-12 f(on) (Symmetric) A∈IRm f∈R SMA-HPC⊙2003MT Finite Differences 6
Numerical Finite Differences Solution Solution Is A non-singular For any 0 01,02 0 2410△a2( (2+(02-01-1)2+ 7=2 Hence vT A v>0, for any v#0(A is SPD)N9 Ai=f i exists and is unique N10 SMA-HPC⊙2003MT Finite Differences 7
Numerical Finite Differences Solution Example um2=(3x+x2)e,x∈(0,1) with u(0)=u(1)=0 ake=5,△a=1/6 SMA-HPC⊙2003MT Finite Differences 8
Numerical Finite Differences Solution Example SMA-HPC⊙2003MT Finite Differences 9