8 years, 80 days

## How do I correct this code?...

Maple 2016

Hello everyone.and complements

Please I am trying to obtain series expansion of the expression below in u but encounter difficulties particularly when b=0. I am very optimistic that when b=0 there will be a result not division by 0. Can I get help on the code?

Thank you in anticipation of your quick and positive responses and suggestions

```# for k=2 CHEBY HYBRID WITH mu=(1-(1/2)*sqrt(2)))) AND v=(1+(1/2)*sqrt(2))))
restart:
omega:=u/h:
t:=(sum(a[j]*x^j,j=0..3)+a[4]*sin(omega*x)+a[5]*cos(omega*x)):
F:=diff(t,x):
G:=diff(t,x,x):
p1:=simplify(eval(t,x=q))=y[n]:
p2:=simplify(eval(t,x=q+(1-(1/2)*sqrt(2))*h))=y[n+mu]:
p3:=simplify(eval(t,x=q+h))=y[n+1]:
p4:=simplify(eval(t,x=q+(1+(1/2)*sqrt(2))*h))=y[n+v]:
p5:=simplify(eval(F,x=q+2*h))=f[n+2]:
p6:=simplify(eval(G,x=q+2*h))=g[n+2]:

vars:= seq(a[i],i=0..5):
Cc:=eval(<vars>, solve({p||(1..6)}, {vars})):
for i from 1 to 6 do
a[i-1]:=Cc[i]:
end do:
Cf:=t:

K:=collect(combine(simplify(eval(Cf,x=q+2*h),size),trig),{y[n],y[n+mu],y[n+1],y[n+v],f[n+2], g[n+2]},factor):

Num := numer(K):
Den := denom(K):

N := 20:   # order of expansion
Num_N :=(convert(series(Num, u, N),polynom)):
Den_N := (convert(series(Den, u, N),polynom)):
b:=y[n+2]=(convert(series(Num_N/Den_N, u, N),polynom)):

eval(b,u=0); ```

## Jacobian elliptic functions...

Maple 2016

Please can someone help with maple comand to obtain Jacobian elliptic functions particularly in code editing region?

## Series Expansion...

Maple 2016

Hello everyone.

Please I am trying to obtain series expansion of the expression below in u and v up to order 30 but encounter difficulties cum maple is slow to display solution. Can I get help on the code and what to do to optimize the displayed time of maple?

Thank you in anticipation of your quick and positive responses and suggestions.

convert(series(convert(series((y[n]+((-8 h u^2 v^2-4 u^3 sin(u) h+2 sin(2 u) h u^3+2 sin(2 v) h v^3-4 v^3 h sin(v)+2 v^3 h sin(2 u+v)+2 u^3 h sin(u-2 v)+2 u^3 h sin(u+2 v)-2 v^3 h sin(2 u-v)-u^3 h sin(2 u+2 v)-v^3 h sin(2 u+2 v)-u^3 h sin(2 u-2 v)+v^3 h sin(2 u-2 v)+4 h u^3 v^2 sin(2 u)+4 h u^2 v^3 sin(2 v)-4 h u^3 v^2 sin(u-v)+4 h u^2 v^3 sin(u-v)-4 h u^3 v^2 sin(u+v)-4 h u^2 v^3 sin(u+v)+4 h u^2 v^2 cos(u)+4 h u^2 v^2 cos(2 u)+4 h u^2 v^2 cos(2 v)+4 h u^2 v^2 cos(v)-4 h u^3 v cos(2 u-v)-2 h u^2 v^2 cos(2 u-v)+2 h u v^3 cos(2 u-v)+4 h u^3 v cos(2 u+v)-2 h u^2 v^2 cos(2 u+v)-2 h u v^3 cos(2 u+v)+2 h u^3 v cos(u-2 v)-2 h u^2 v^2 cos(u-2 v)-4 h u v^3 cos(u-2 v)-2 h u^3 v cos(u+2 v)-2 h u^2 v^2 cos(u+2 v)+4 h u v^3 cos(u+2 v)+4 h u^3 v cos(u-v)+4 h u v^3 cos(u-v)-4 h u^3 v cos(u+v)-4 h u v^3 cos(u+v)+4 u sin(u) v^2 h-2 sin(2 u) h u v^2-2 sin(2 v) h u^2 v+4 v h sin(v) u^2-2 v u^2 h sin(2 u+v)-2 u v^2 h sin(u-2 v)-2 u v^2 h sin(u+2 v)+2 v u^2 h sin(2 u-v)+v u^2 h sin(2 u+2 v)+u v^2 h sin(2 u+2 v)-v u^2 h sin(2 u-2 v)+u v^2 h sin(2 u-2 v)) f[n])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)+((-8 h u^2 v^2+8 u^3 sin(u) h-4 sin(2 u) h u^3-4 sin(2 v) h v^3+8 v^3 h sin(v)-4 v^3 h sin(2 u+v)-4 u^3 h sin(u-2 v)-4 u^3 h sin(u+2 v)+4 v^3 h sin(2 u-v)+2 u^3 h sin(2 u+2 v)+2 v^3 h sin(2 u+2 v)+2 u^3 h sin(2 u-2 v)-2 v^3 h sin(2 u-2 v)+8 h u^3 v^2 sin(u)+8 h u^2 v^3 sin(v)-4 h u^3 v^2 sin(2 u+v)+4 h u^2 v^3 sin(2 u+v)+4 h u^3 v^2 sin(u-2 v)+4 h u^2 v^3 sin(u-2 v)+4 h u^3 v^2 sin(u+2 v)-4 h u^2 v^3 sin(u+2 v)-4 h u^3 v^2 sin(2 u-v)-4 h u^2 v^3 sin(2 u-v)+8 h u^2 v^2 cos(u)+8 h u^2 v^2 cos(v)+4 h u^3 v cos(2 u-v)-4 h u^2 v^2 cos(2 u-v)-8 h u v^3 cos(2 u-v)-4 h u^3 v cos(2 u+v)-4 h u^2 v^2 cos(2 u+v)+8 h u v^3 cos(2 u+v)-8 h u^3 v cos(u-2 v)-4 h u^2 v^2 cos(u-2 v)+4 h u v^3 cos(u-2 v)+8 h u^3 v cos(u+2 v)-4 h u^2 v^2 cos(u+2 v)-4 h u v^3 cos(u+2 v)-2 h u^3 v cos(2 u+2 v)+4 h u^2 v^2 cos(2 u+2 v)-2 h u v^3 cos(2 u+2 v)+2 h u^3 v cos(2 u-2 v)+4 h u^2 v^2 cos(2 u-2 v)+2 h u v^3 cos(2 u-2 v)-8 u sin(u) v^2 h+4 sin(2 u) h u v^2+4 sin(2 v) h u^2 v-8 v h sin(v) u^2+4 v u^2 h sin(2 u+v)+4 u v^2 h sin(u-2 v)+4 u v^2 h sin(u+2 v)-4 v u^2 h sin(2 u-v)-2 v u^2 h sin(2 u+2 v)-2 u v^2 h sin(2 u+2 v)+2 v u^2 h sin(2 u-2 v)-2 u v^2 h sin(2 u-2 v)) f[n+1])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)+((-8 h u^2 v^2-4 u^3 sin(u) h+2 sin(2 u) h u^3+2 sin(2 v) h v^3-4 v^3 h sin(v)+2 v^3 h sin(2 u+v)+2 u^3 h sin(u-2 v)+2 u^3 h sin(u+2 v)-2 v^3 h sin(2 u-v)-u^3 h sin(2 u+2 v)-v^3 h sin(2 u+2 v)-u^3 h sin(2 u-2 v)+v^3 h sin(2 u-2 v)+4 h u^3 v^2 sin(2 u)+4 h u^2 v^3 sin(2 v)-4 h u^3 v^2 sin(u-v)+4 h u^2 v^3 sin(u-v)-4 h u^3 v^2 sin(u+v)-4 h u^2 v^3 sin(u+v)+4 h u^2 v^2 cos(u)+4 h u^2 v^2 cos(2 u)+4 h u^2 v^2 cos(2 v)+4 h u^2 v^2 cos(v)-4 h u^3 v cos(2 u-v)-2 h u^2 v^2 cos(2 u-v)+2 h u v^3 cos(2 u-v)+4 h u^3 v cos(2 u+v)-2 h u^2 v^2 cos(2 u+v)-2 h u v^3 cos(2 u+v)+2 h u^3 v cos(u-2 v)-2 h u^2 v^2 cos(u-2 v)-4 h u v^3 cos(u-2 v)-2 h u^3 v cos(u+2 v)-2 h u^2 v^2 cos(u+2 v)+4 h u v^3 cos(u+2 v)+4 h u^3 v cos(u-v)+4 h u v^3 cos(u-v)-4 h u^3 v cos(u+v)-4 h u v^3 cos(u+v)+4 u sin(u) v^2 h-2 sin(2 u) h u v^2-2 sin(2 v) h u^2 v+4 v h sin(v) u^2-2 v u^2 h sin(2 u+v)-2 u v^2 h sin(u-2 v)-2 u v^2 h sin(u+2 v)+2 v u^2 h sin(2 u-v)+v u^2 h sin(2 u+2 v)+u v^2 h sin(2 u+2 v)-v u^2 h sin(2 u-2 v)+u v^2 h sin(2 u-2 v)) f[n+2])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)+((-6 u^2 h^2-6 v^2 h^2-4 cos(2 u) h^2 u^2 v^2-4 cos(2 v) h^2 u^2 v^2+8 v^2 u^2 h^2 cos(u-v)+8 v^2 u^2 h^2 cos(u+v)+8 u sin(u) v^2 h^2+8 sin(2 u) h^2 u v^2+8 sin(2 v) h^2 u^2 v+8 v h^2 sin(v) u^2+4 v u^2 h^2 sin(2 u+v)-4 u v^2 h^2 sin(2 u+v)+8 v u^2 h^2 sin(u-v)-8 sin(u-v) h^2 u v^2-8 v u^2 h^2 sin(u+v)-8 sin(u+v) h^2 u v^2+4 v u^2 h^2 sin(u-2 v)+4 u v^2 h^2 sin(u-2 v)-4 v u^2 h^2 sin(u+2 v)+4 u v^2 h^2 sin(u+2 v)-4 v u^2 h^2 sin(2 u-v)-4 u v^2 h^2 sin(2 u-v)-4 u v h^2 cos(2 u-v)+4 u v h^2 cos(2 u+v)-4 u v h^2 cos(u-2 v)+4 u v h^2 cos(u+2 v)-2 u v h^2 cos(2 u+2 v)+2 u v h^2 cos(2 u-2 v)+8 cos(u-v) h^2 u v-8 cos(u+v) h^2 u v-8 v^2 u^2 h^2+8 h^2 cos(u) u^2-2 cos(2 u) h^2 u^2+6 cos(2 u) h^2 v^2+6 cos(2 v) h^2 u^2-2 cos(2 v) h^2 v^2+8 h^2 cos(v) v^2-4 v^2 h^2 cos(2 u-v)-4 v^2 h^2 cos(2 u+v)-4 u^2 h^2 cos(u-2 v)-4 u^2 h^2 cos(u+2 v)+u^2 h^2 cos(2 u+2 v)+v^2 h^2 cos(2 u+2 v)+u^2 h^2 cos(2 u-2 v)+v^2 h^2 cos(2 u-2 v)) g[n])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)+((6 u^2 h^2+6 v^2 h^2+4 cos(2 u) h^2 u^2 v^2+4 cos(2 v) h^2 u^2 v^2-8 v^2 u^2 h^2 cos(u-v)-8 v^2 u^2 h^2 cos(u+v)-8 u sin(u) v^2 h^2-8 sin(2 u) h^2 u v^2-8 sin(2 v) h^2 u^2 v-8 v h^2 sin(v) u^2-4 v u^2 h^2 sin(2 u+v)+4 u v^2 h^2 sin(2 u+v)-8 v u^2 h^2 sin(u-v)+8 sin(u-v) h^2 u v^2+8 v u^2 h^2 sin(u+v)+8 sin(u+v) h^2 u v^2-4 v u^2 h^2 sin(u-2 v)-4 u v^2 h^2 sin(u-2 v)+4 v u^2 h^2 sin(u+2 v)-4 u v^2 h^2 sin(u+2 v)+4 v u^2 h^2 sin(2 u-v)+4 u v^2 h^2 sin(2 u-v)+4 u v h^2 cos(2 u-v)-4 u v h^2 cos(2 u+v)+4 u v h^2 cos(u-2 v)-4 u v h^2 cos(u+2 v)+2 u v h^2 cos(2 u+2 v)-2 u v h^2 cos(2 u-2 v)-8 cos(u-v) h^2 u v+8 cos(u+v) h^2 u v+8 v^2 u^2 h^2-8 h^2 cos(u) u^2+2 cos(2 u) h^2 u^2-6 cos(2 u) h^2 v^2-6 cos(2 v) h^2 u^2+2 cos(2 v) h^2 v^2-8 h^2 cos(v) v^2+4 v^2 h^2 cos(2 u-v)+4 v^2 h^2 cos(2 u+v)+4 u^2 h^2 cos(u-2 v)+4 u^2 h^2 cos(u+2 v)-u^2 h^2 cos(2 u+2 v)-v^2 h^2 cos(2 u+2 v)-u^2 h^2 cos(2 u-2 v)-v^2 h^2 cos(2 u-2 v)) g[n+2])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)),u=0,32),polynom),v=0,32),polynom);

## Computational and Numerical Analyst...

Hello everyone.

Please can I meet with Computational or/and Numerical anlysts that have worked or working on the algorihms particularly (Runge Kutta Nystrom, Block multistep methods including hybrid and Block Boundaru Value methods) for the solution of both IVP and BVP.

I will appreciante if I can learn from them and possibly collaborate with them. Thank you in anticipation of your positive response.

## Code Correction...

Maple 2016

Please I am having problem with this code particularly the last subroutine

#subroutine 1

restart;
Digits:=30:

f:=proc(n)
-25*y[n]+12*cos(x[n]):
end proc:

#subroutine 2

e1:=y[n+4] = -y[n]+2*y[n+2]+((1/15)*h^2+(2/945)*h^2*u^2+(1/56700)*h^2*u^4-(1/415800)*h^2*u^6-(167/833976000)*h^2*u^8-(2633/245188944000)*h^2*u^10-(2671/5557616064000)*h^2*u^12-(257857/13304932857216000)*h^2*u^14-(3073333/4215002729166028800)*h^2*u^16)*f(n)+((16/15)*h^2-(8/945)*h^2*u^2-(1/14175)*h^2*u^4+(1/103950)*h^2*u^6+(167/208494000)*h^2*u^8+(2633/61297236000)*h^2*u^10+(2671/1389404016000)*h^2*u^12+(257857/3326233214304000)*h^2*u^14+(3073333/1053750682291507200)*h^2*u^16)*f(n+1)+((26/15)*h^2+(4/315)*h^2*u^2+(1/9450)*h^2*u^4-(1/69300)*h^2*u^6-(167/138996000)*h^2*u^8-(2633/40864824000)*h^2*u^10-(2671/926269344000)*h^2*u^12-(257857/2217488809536000)*h^2*u^14-(3073333/702500454861004800)*h^2*u^16)*f(n+2)+((16/15)*h^2-(8/945)*h^2*u^2-(1/14175)*h^2*u^4+(1/103950)*h^2*u^6+(167/208494000)*h^2*u^8+(2633/61297236000)*h^2*u^10+(2671/1389404016000)*h^2*u^12+(257857/3326233214304000)*h^2*u^14+(3073333/1053750682291507200)*h^2*u^16)*f(n+3)+((1/15)*h^2+(2/945)*h^2*u^2+(1/56700)*h^2*u^4-(1/415800)*h^2*u^6-(167/833976000)*h^2*u^8-(2633/245188944000)*h^2*u^10-(2671/5557616064000)*h^2*u^12-(257857/13304932857216000)*h^2*u^14-(3073333/4215002729166028800)*h^2*u^16)*f(n+4):

e2:=y[n+3] = -y[n+1]+2*y[n+2]+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(n)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(n+1)+((97/120)*h^2-(31/10080)*h^2*u^2-(67/302400)*h^2*u^4-(109/8870400)*h^2*u^6-(18127/31135104000)*h^2*u^8-(64931/2615348736000)*h^2*u^10-(9701/9880206336000)*h^2*u^12-(20832397/567677135241216000)*h^2*u^14-(11349439/8646159444443136000)*h^2*u^16)*f(n+2)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(n+3)+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(n+4):

e3:=h*delta[n] = (-149/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[n]+(128/21+(32/245)*u^2+(2648/169785)*u^4+(1118492/695269575)*u^6+(14310311/87603966450)*u^8+(170868550903/10320623287474500)*u^10)*y[n+1]+(-107/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[n+2]+(-(67/1260)*h^2+(1241/198450)*h^2*u^2+(277961/366735600)*h^2*u^4+(26460409/333729396000)*h^2*u^6+(1363374533/168199615584000)*h^2*u^8+(16323847966961/19815596711951040000)*h^2*u^10)*f(n)+((188/105)*h^2+(5078/99225)*h^2*u^2+(556159/91683900)*h^2*u^4+(51834031/83432349000)*h^2*u^6+(67782373/1078202664000)*h^2*u^8+(1854079193287/291405833999280000)*h^2*u^10)*f(n+1)+((31/90)*h^2+(341/33075)*h^2*u^2+(79361/61122600)*h^2*u^4+(23456627/166864698000)*h^2*u^6+(1228061399/84099807792000)*h^2*u^8+(14797833720283/9907798355975520000)*h^2*u^10)*f(n+2)+(-(4/105)*h^2-(46/14175)*h^2*u^2-(809/1871100)*h^2*u^4-(27827/567567000)*h^2*u^6-(637171/122594472000)*h^2*u^8-(33500737/62523180720000)*h^2*u^10)*f(n+3)+((1/252)*h^2+(23/28350)*h^2*u^2+(809/7484400)*h^2*u^4+(27827/2270268000)*h^2*u^6+(637171/490377888000)*h^2*u^8+(33500737/250092722880000)*h^2*u^10)*f(n+4):

e4:=y[3] = -y[1]+2*y[2]+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(0)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(1)+((97/120)*h^2-(31/10080)*h^2*u^2-(67/302400)*h^2*u^4-(109/8870400)*h^2*u^6-(18127/31135104000)*h^2*u^8-(64931/2615348736000)*h^2*u^10-(9701/9880206336000)*h^2*u^12-(20832397/567677135241216000)*h^2*u^14-(11349439/8646159444443136000)*h^2*u^16)*f(2)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(3)+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(4):

e5:=h*delta[0] = (-149/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[0]+(128/21+(32/245)*u^2+(2648/169785)*u^4+(1118492/695269575)*u^6+(14310311/87603966450)*u^8+(170868550903/10320623287474500)*u^10)*y[1]+(-107/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[2]+(-(67/1260)*h^2+(1241/198450)*h^2*u^2+(277961/366735600)*h^2*u^4+(26460409/333729396000)*h^2*u^6+(1363374533/168199615584000)*h^2*u^8+(16323847966961/19815596711951040000)*h^2*u^10)*f(0)+((188/105)*h^2+(5078/99225)*h^2*u^2+(556159/91683900)*h^2*u^4+(51834031/83432349000)*h^2*u^6+(67782373/1078202664000)*h^2*u^8+(1854079193287/291405833999280000)*h^2*u^10)*f(1)+((31/90)*h^2+(341/33075)*h^2*u^2+(79361/61122600)*h^2*u^4+(23456627/166864698000)*h^2*u^6+(1228061399/84099807792000)*h^2*u^8+(14797833720283/9907798355975520000)*h^2*u^10)*f(2)+(-(4/105)*h^2-(46/14175)*h^2*u^2-(809/1871100)*h^2*u^4-(27827/567567000)*h^2*u^6-(637171/122594472000)*h^2*u^8-(33500737/62523180720000)*h^2*u^10)*f(3)+((1/252)*h^2+(23/28350)*h^2*u^2+(809/7484400)*h^2*u^4+(27827/2270268000)*h^2*u^6+(637171/490377888000)*h^2*u^8+(33500737/250092722880000)*h^2*u^10)*f(4):

#subroutine 3

inx:=0:
ind:=0:
iny:=1:
h:=Pi/4.0:
n:=0:
omega:=5:
u:=omega*h:
N:=solve(h*p = 500*Pi/2, p):

c:=1:
for j from 0 to 5 do
t[j]:=inx+j*h:
end do:
#e||(1..6);
vars:=y[n+1],y[n+2],y[n+3],delta[n],y[n+4]:

printf("%6s%15s%15s%15s\n",
"h","Num.y","Ex.y","Error y");
for k from 1 to N do

par1:=x[0]=t[0],x[1]=t[1],x[2]=t[2],x[3]=t[3],x[4]=t[4],x[5]=t[5]:
par2:=y[n]=iny,delta[n]=ind:

res:=eval(<vars>, fsolve(eval({e||(1..5)},[par1,par2]), {vars}));

for i from 1 to 5 do
exy:=eval(0.5*cos(5*c*h)+0.5*cos(c*h)):
printf("%6.5f%17.9f%15.9f%13.5g\n",
h*c,res[i],exy,abs(res[i]-exy)):

c:=c+1:
end do:
iny:=res[5]:
inx:=t[5]:
for j from 0 to 5 do
t[j]:=inx + j*h:
end do:
end do:

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