Appendix.
The Mathematica pseudocodes of block Adams family for computing
time-tested problem 1 and time-tested problem 2 is given beneath.
The block Adams-Bashforth of the block Adams family.
g[t_]=exact result
h=x[n]=given taking off parameters
t= the result of the above parameters
g[1]=g[0]+h(g’[0])+(h^2/2)g”[0]+(h^3/6)g”’[0]
g[2]=g[1]+h(g’[x[n]])+(h^2/2)g”[x[n]]+(h^3/6)g”’[x[n]]
g[3]=g[2]+h(g’[x[n]+h])+(h^2/2)g”[x[n]+h]+(h^3/6)g”’[x[n]+h]
g[4]=g[3]+h(g’[x[n]+2h])+(h^2/2)g”[x[n]+2h]+(h^3/6)g”’[x[n]+2h]
g[5]=g[4]+h(g’[x[n]+3h])+(h^2/2)g”[x[n]+3h]+(h^3/6)g”’[x[n]+3h]
t=x[n]+2h
g[4]=g[3]+h((53/12)g’[t-x[n]]-(16/3)g’[t-(x[n]+h)]+(23/12)g’[t-(x[n]+2h)])
t=x[n]+4h
g[6]=g[4]+h((37/3)g’[t-x[n]]-(50/3)g’[t-(x[n]+h)]+(19/3)g’[t-(x[n]+2h)])
t=x[n]+6h
g[8]=g[5]+h((99/4)g’[t-x[n]]-(36)g’[t-(x[n]+h)]+(57/4)g’[t-(x[n]+2h)])
t=x[n]+5h
g[7]=g[6]+h((53/12)g’[t-x[n]]-(16/3)g’[t-(x[n]+h)]+(23/12)g’[t-(x[n]+2h)])
t=x[n]+7h
g[9]=g[7]+h((37/3)g’[t-x[n]]-(50/3)g’[t-(x[n]+h)]+(19/3)g’[t-(x[n]+2h)])
t=x[n]+9h
g[11]=g[8]+h((99/4)g’[t-x[n]]-(36)g’[t-(x[n]+h)]+(57/4)g’[t-(x[n]+2h)])
t=x[n]+8h
g[10]=g[9]+h((53/12)g’[t-x[n]]-(16/3)g’[t-(x[n]+h)]+(23/12)g’[t-(x[n]+2h)])
t=x[n]+10h
g[12]=g[10]+h((37/3)g’[t-x[n]]-(50/3)g’[t-(x[n]+h)]+(19/3)g’[t-(x[n]+2h)])
t=x[n]+12h
g[14]=g[11]+h((99/4)g’[t-x[n]]-(36)g’[t-(x[n]+h)]+(57/4)g’[t-(x[n]+2h)])
The block Adams-Moulton method of the block Adams family.
y[u_]=exact result
h=x[n]=given taking off parameters
u= the result of the above parameters
y[1]=y[0]+h(y’[0])+(h^2/2)y”[0]+(h^3/6)y”’[0]
y[2]=y[1]+h(y’[x[n]])+(h^2/2)y”[x[n]]+(h^3/6)y”’[x[n]]
y[3]=y[2]+h(y’[x[n]+h])+(h^2/2)y”[x[n]+h]+(h^3/6)y”’[x[n]+h]
y[4]=y[3]+h(y’[x[n]+2h])+(h^2/2)y”[x[n]+2h]+(h^3/6)y”’[x[n]+2h]
y[5]=y[4]+h(y’[x[n]+3h])+(h^2/2)y”[x[n]+3h]+(h^3/6)y”’[x[n]+3h]
u=x[n]+2h
y[4]=y[1]+h((57/4)y’[u+x[n]]-(18)y’[u+x[n]+h]+(27/4)y’[u+x[n]+2h])
u=x[n]+4h
y[6]=y[2]+h((44/3)y’[u+x[n]]-(52/3)y’[u+x[n]+h]+(20/3)y’[u+x[n]+2h])
u=x[n]+6h
y[8]=y[3]+h((175/12)y’[u+x[n]]-(50/3)y’[u+x[n]+h]+(85/12)y’[u+x[n]+2h])
u=x[n]+5h
y[7]=y[4]+h((57/4)y’[u+x[n]]-(18)y’[u+x[n]+h]+(27/4)y’[u+x[n]+2h])
u=x[n]+7h
y[9]=y[5]+h((44/3)y’[u+x[n]]-(52/3)y’[u+x[n]+h]+(20/3)y’[u+x[n]+2h])
u=x[n]+9h
y[11]=y[6]+h((175/12)y’[u+x[n]]-(50/3)y’[u+x[n]+h]+(85/12)y’[u+x[n]+2h])
u=x[n]+8h
y[10]=y[7]+h((57/4)y’[u+x[n]]-(18)y’[u+x[n]+h]+(27/4)y’[u+x[n]+2h])
u=x[n]+10h
y[12]=y[8]+h((44/3)y’[u+x[n]]-(52/3)y’[u+x[n]+h]+(20/3)y’[u+x[n]+2h])
u=x[n]+12h
y[14]=y[9]+h((175/12)y’[u+x[n]]-(50/3)y’[u+x[n]+h]+(85/12)y’[u+x[n]+2h])