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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Differenci\341legyenlet   " }
{MPLTEXT 0 21 52 "(Delta-a^2)*Phi(x,y,z)=-4*Pi*rho:rho=exp(-r)/(8*Pi):
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "G\366mbszimmetrikus megold
\341sra  " }{MPLTEXT 0 21 77 " phi(r)=r*Phi(r),Diff(phi,r$2)-a^2*phi=-
4*Pi*r*rho, phi(0)=0,phi(infinity)=0:" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 17 "Diszkretiz\341lva   " }{MPLTEXT 0 21 69 " phi[i+1]-(2+a^2
*delta^2)*phi[i]+phi[i-1]=-delta^2*(r*exp(-r))[i]/2: " }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 19 "Az egzakt megold\341s " }{MPLTEXT 1 0 51 
"phi:=r->(exp(-a*r)-exp(-r)*(1+b*r/2))/b^2:b:=1-a^2:" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 50 "simplify(diff(phi(r),r$2)-a^2*phi(r)+r*exp(-r)/2
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "a:=3.:mx:=5*a:\npl1:=
plot(phi(x),x=0..mx):display(pl1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 84 "A numerikus megold\341s a tridiagon\341lis egyenletrendszer el
\365re-h\341tra helyettes\355t\351s\351vel\n" }{MPLTEXT 1 0 31 "mx:=15
.:n:=160:delta:=mx/(n+1);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 35 "A tridiagon\341lis m\341trix elk\351sz\355t\351se\n" }
{MPLTEXT 1 0 116 "alpha:=1.:beta:=-(2+delta^2*a^2):gama:=1.:\nfor i fr
om 1 to n do\nx[i]:=i*delta:\nd[i]:=-delta^2*x[i]*exp(-x[i])/2:\nod:" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "H\341tra helyettes\355t\351s\n \+
" }{MPLTEXT 1 0 147 "g[n-1]:=-alpha/beta:h[n-1]:=d[n]/beta:\nfor i fro
m n-1 to 2 by -1 do\ng[i-1]:=-alpha/(beta+gama*g[i]):\nh[i-1]:=(d[i]-g
ama*h[i])/(beta+gama*g[i]):\nod:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
20 "El\365re helyettes\355t\351s\n" }{MPLTEXT 1 0 97 "psi[1]:=(d[1]-ga
ma*h[1])/(beta+gama*g[1]):\nfor i from 1 to n-1 do\npsi[i+1]:=g[i]*psi
[i]+h[i]:\nod:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "pl1:=plo
t(phi(x),x=0..mx):\nl := [[ x[k], psi[k]] $k=1..n]:\npl2:=plot(l, x=0.
.mx, style=point,symbol=circle):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 
"display(\{pl1,pl2\});" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "l := [[ x
[k], psi[k]-phi(x[k])] $k=1..n]:\nplot(l, x=0..mx, style=point,symbol=
circle);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "9 0
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