Решение краевой задачи на графе методом Ритца

w[i]:=0;

end;

i:=n[1]-1;

c[i]:=c[i]/b[i];

d[i]:=d[i]/b[i];

e[i]:=e[i]/b[i];

y[i]:=y[i]/b[i];

b[i]:=1;

b[i+1]:=b[i+1]-c[i]*a[i];

c[i+1]:=c[i+1]-d[i]*a[i];

e[i+1]:=e[i+1]-e[i]*a[i];

y[i+1]:=y[i+1]-y[i]*a[i];

a[i]:=0;

a[i+1]:=a[i+1]-c[i]*v[i];

b[i+2]:=b[i+2]-d[i]*v[i];

e[i+2]:=e[i+2]-e[i]*v[i];

y[i+2]:=y[i+2]-y[i]*v[i];

v[i]:=0;

w[i+1]:=w[i+1]-c[i]*w[i];

w[i+2]:=w[i+2]-d[i]*w[i];

b[n[1]+n[2]]:=b[n[1]+n[2]]-e[i]*w[i];

y[n[1]+n[2]]:=y[n[1]+n[2]]-y[i]*w[i];

w[i]:=0;

for i:=n[1] to n[1]+n[2]-3 do

begin

c[i]:=c[i]/b[i];

e[i]:=e[i]/b[i];

y[i]:=y[i]/b[i];

b[i]:=1;

b[i+1]:=b[i+1]-c[i]*a[i];

e[i+1]:=e[i+1]-e[i]*a[i];

y[i+1]:=y[i+1]-y[i]*a[i];

a[i]:=0;

w[i+1]:=w[i+1]-c[i]*w[i];

b[n[1]+n[2]]:=b[n[1]+n[2]]-e[i]*w[i];

y[n[1]+n[2]]:=y[n[1]+n[2]]-y[i]*w[i];

w[i]:=0;

end;

i:=n[1]+n[2]-2;

c[i]:=c[i]/b[i];

e[i]:=e[i]/b[i];

y[i]:=y[i]/b[i];

b[i]:=1;

b[i+1]:=b[i+1]-c[i]*a[i];

c[i+1]:=e[i+1]-e[i]*a[i];

y[i+1]:=y[i+1]-y[i]*a[i];

a[i]:=0;

a[i+1]:=a[i+1]-b[i+1]*w[i];

b[n[1]+n[2]]:=b[n[1]+n[2]]-c[i]*w[i];

y[n[1]+n[2]]:=y[n[1]+n[2]]-y[i]*w[i];

w[i]:=0;

for i:=n[1]+n[2]-1 to n[1]+n[2]+n[3]-3 do

begin

c[i]:=c[i]/b[i];

y[i]:=y[i]/b[i];

b[i]:=1;

b[i+1]:=b[i+1]-c[i]*a[i];

y[i+1]:=y[i+1]-y[i]*a[i];

a[i]:=0;

end;

y[nn]:=y[nn]/b[nn];

b[nn]:=1;

end;

procedure obratno;

var

i: integer;

begin

for i:=1 to nn do cf[i]:=0;

cf[nn]:=y[nn];

for i:=nn-1 downto n[1]+n[2]-2 do cf[i]:=y[i]-c[i]*cf[i+1];

for i:=n[1]+n[2]-3 downto n[1] do cf[i]:=y[i]-cf[n[1]+n[2]]*e[i]-c[i]*cf[i+1];

for i:=n[1]-1 downto 1 do cf[i]:=y[i]-c[i]*cf[i+1]-cf[n[1]+n[2]]*e[i]-cf[n[1]+1]*d[i];

end;

procedure print_vect(vectors: string);

var

i, nn: integer;

vec: textfile;

fname: string;

begin

nn:=n[1]+n[2]+n[3]-2;

fname:=vectors+'.txt';

assignfile(vec,fname);

rewrite(vec);

writeln(vec,'a:');

for i:=1 to nn-1 do writeln(vec,a[i]:7:4);

writeln(vec,'b:');

for i:=1 to nn do writeln(vec,b[i]:7:4);

writeln(vec,'c:');

for i:=1 to nn-1 do writeln(vec,c[i]:7:4);

writeln(vec,'d:');

for i:=1 to n[1]-1 do writeln(vec,d[i]:7:4);

writeln(vec,'e:');

for i:=1 to n[1]+n[2]-2 do writeln(vec,e[i]:7:4);

writeln(vec,'v:');

for i:=1 to n[1]-1 do writeln(vec,v[i]:7:4);

writeln(vec,'w:');

for i:=1 to n[1]+n[2]-2 do writeln(vec,w[i]:7:4);

writeln(vec,'y:');

for i:=1 to n[1]+n[2]+n[3]-2 do writeln(vec,y[i]:7:4);

writeln(vec,'cf:');

for i:=1 to n[1]+n[2]+n[3]-2 do writeln(vec,cf[i]:7:4);

closefile(vec);

end;

begin // resh_sist

nn:=n[1]+n[2]+n[3]-2;

b[1]:=matr[1,1];

c[1]:=matr[1,2];

b[nn]:=matr[nn,nn];

a[nn-1]:=matr[nn,nn-1];

for i:=2 to nn-1 do

for j:=(i-1) to (i+1) do

begin

if i=j then b[i]:=matr[i,j]

else

if i=(j-1) then c[i]:=matr[i,j]

else if j=(i-1) then a[i-1]:=matr[i,j];

end;

for i:=1 to n[1] do d[i]:=0;

d[1]:=matr[1,n[1]+1];

for i:=1 to n[1]+n[2]-1 do e[i]:=0;

e[1]:=matr[1,n[1]+n[2]];

for i:=1 to n[1] do v[i]:=0;

v[1]:=matr[n[1]+1,1];

for i:=1 to n[1]+n[2]-1 do w[i]:=0;

w[1]:=matr[n[1]+n[2],1];

for i:=1 to nn do y[i]:=pr_ch[i];

print_vect('vec1');

gauss;

print_vect('vec2');

obratno;

print_vect('vec3');

end;

procedure TForm1.Button3Click(Sender: TObject);

var

i, j: integer;

r: real;

m: real;

q: integer;

begin

for i:=0 to n[1] do series1.AddXY(x1[i],u_toch(x1[i],1));

for i:=0 to n[2] do series3.AddXY(x2[i],u_toch(x2[i],2));

for i:=0 to n[3] do series5.AddXY(x3[i],u_toch(x3[i],3));

q:=2;

m:=h[1]/q;

for i:=0 to (n[1]-1)*q+1 do

begin

r:=cf[1]*splain(x1[i],0,1);

for j:=1 to n[1]-1 do r:=r+cf[j+1]*splain(x1[0]+m*i,j,1);

series2.AddXY(x1[0]+m*i,r);

end;

series2.AddXY(x1[n[1]],u_toch(l[1],1));

m:=h[2]/q;

for i:=0 to (n[2]-1)*q+1 do

begin

r:=cf[1]*splain(x2[i],0,2);

for j:=1 to n[2]-1 do r:=r+cf[j+n[1]]*splain(x2[0]+m*i,j,2);

series4.AddXY(x2[0]+m*i,r);

end;

series4.AddXY(x2[n[2]],u_toch(l[2],2));

m:=h[3]/q;

for i:=0 to (n[3]-1)*q+1 do

begin

r:=cf[1]*splain(x3[i],0,3);

for j:=1 to n[3]-1 do r:=r+cf[j+n[1]+n[2]-1]*splain(x3[0]+m*i,j,3);

series6.AddXY(x3[0]+m*i,r);

end;

series6.AddXY(x3[n[3]],u_toch(l[3],3));

end;

procedure TForm1.Button2Click(Sender: TObject);

begin

sost_sist;

resh_sist;

showmessage('ok');

end;

end.

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