NumerovSol10[gcn_,x0_,xend_,zstart0_,zstart1_,n_]:=Module[{a,w,d,h,x,m,z,g,g0,g1},  
d={{0,0,0,0,0,0,0,0,0,0,0,0},
{0,0,0,0,0,0,0,0,0,0,0,0},
{4/125,11/125,0,0,0,0,0,0,0,0,0,0},
{19/384,25/64,-(25/384),0,0,0,0,0,0,0,0,0},
{5995/201684,18975/33614,-(25875/67228),4880/50421,0,0,0,0,0,0,0,0},
{925501/21056436,3562265/3509406,-(38885125/42112872),-(962420/5264109),8460781/14037624,0,0,0,0,0,0,0},
{-(10212631609250341/328176241146304817),-(323995948240341556/892306248023092307),180826714877251145/878825618452095912,-(309495208666636268/211256158281753825),907593860888833066/705545727701934129,30050427761143/117384397430625,0,0,0,0,0,0},
{-(72578916496589770/489387826625308489),-(167412866190232198/228720317429147187),441765791889659475/506442929644371968,-(834559362480725660/434718393596130577),333579114865186823/186582562532336998,64300433411319131/247081571517383771,149598300269611654/279146853601869633,0,0,0,0,0},
{-(672479649026724/134701603063519825),-(11985261160989701/252507407350507240),-(44934162477377361/480555274161507322),-(79996279240647685/172818890501479699),978003635897823281/1593365786976807543,-(152600061269435925/775432683829886734),-(18168702228157858/272638963484159197),23522741/142787820,0,0,0,0},
{12672884057427077/235325768447454068,161331663985134442/281098672238950563,-(152201621958835429/254532091961693096),539773756678309788/250123833416985205,-(594158991693243179/436899179941667819),-(151329347593289966/134123470959933563),-(46169611023825497/305761285851099384),204009974645557145/462204329009391299,-(37793577225423153/1079769183138939451),0,0,0},
{-(974604435900431659/608389921149430209),-(492006681657325801/48582687886496281),561443095029958638/47351117731513699,-(202515185920500367/59909259329485212),0,167122059892840043/372951286650427891,256512434121543545/75353830251557493,0,-(31188994765510625/42053596120628014),1882206063/1888012840,0,0},
{-(948213930618720599/200327681653618263),-(386395620984053718/15152585320856519),1357805245118529609/43292681138977384,665881174854371134/236521979347307869,-(702569991355697358/59845516566858131),-(84217125875509289/188026757486446467),5742984473730156307/766153391678093106,-(8669150899145936/71946319200625485),-(47582792218897328/22611700320196581),43220141640625/10882497805641,0,0}};
a={-1,0,1/5,1/2,3/7,2/3,-(2/3),3/4,-(3/4),-(9/10),9/10,1};
w={-(271/4655),317321/612360,0,0,0,2435589/3132080,2435589/3132080,-(8255488/11133045),-(8255488/11133045),276875000/1052662149,276875000/1052662149,-(271/4655)};
h=N[(xend-x0)/n,33];
x=x0+Range[0,n]*h;
m=Length[zstart0];
z=Array[Array[0&,m]&,n+1];
z[[1]]=zstart0;
z[[2]]=zstart1;
g=Array[Array[0&,m]&,12];
g[[2]]=gcn[x[[1]],z[[1]]];
Do[g0=g[[2]];
g1=gcn[x[[k]],z[[k]]];
g=Array[Array[0&,m]&,12];
g[[1]]=g0;g[[2]]=g1;
Do[g[[o]]=gcn[x[[k]]+a[[o]]*h,(1+a[[o]])*z[[k]]-a[[o]]*z[[k-1]]+h^2*d[[o]].g],{o,3,12}];
z[[k+1]]=N[2*z[[k]]-z[[k-1]]+h^2*w.g,33];
z[[k+1]]=Rationalize[z[[k+1]],10^-33],{k,2,n}];
Return[{x,z}]];