Finite Difference Lagrange interpolation Formulas Example Assuming a uniform grid m=1(First derivative) 616 +1 2△x△a △ Forward -2△0 2△ Centered +1 3 2△m△a2△m Backward SMA-HPC⊙2003MT Finite Differences 5
Finite Difference Lagrange interpolation Formulas Example m=2( Second derivative) y+1 2 Centered N2 SMA-HPC⊙2003MT Finite Differences 6
Finite Difference Undetermined coefficients Formulas Start from dmu dam Insert Taylor expansions for v; about a = i 00+0(x;-x)+2v(x1;-)2+…, determine coefficients 8, to maximize accuracy SMA-HPC⊙2003MT Finite Differences 7
Finite Difference Undetermined coefficients Formulas Example m=2, l=r=1, i=0,(uniform spacing Ac) 0=621(0-△a+20-40+0+…) +6v0 +62(0+△m+2n+0"+a(0)+…) SMA-HPC⊙2003MT Finite Differences 8
Finite Difference Undetermined coefficients Formulas Example Equating coefficients of u() k=0→021+6+62=0 k=1→△a(62-621)=0 k=2→22(61+62)=1 Solve 163=-△m2 2 1 3N4 SMA-HPC⊙2003MT Finite Differences 9