Решение краевой задачи на графе методом Ритца
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[n[2]],r,k) )/2;j:=1 to koef*n[2]-1 do_pr_1:=skal_pr_1 + Tt*Asplain(j*hh[2],p,k)*Asplain(j*hh[2],r,k);_pr_1:=skal_pr_1*hh[2];;
: begin_pr_1:=( Tt*Asplain(0,p,k)*Asplain(0,r,k) +*Asplain(x3[n[3]],p,k)*Asplain(x3[n[3]],r,k) )/2;j:=1 to koef*n[3]-1 do_pr_1:=skal_pr_1 + Tt*Asplain(j*hh[3],p,k)*Asplain(j*hh[3],r,k);_pr_1:=skal_pr_1*hh[3];;;_pr:=skal_pr_1;
end;
// правая часть ; p - номер сплайна, k - номер струны
function integral(p, k: integer): real;: integer;, int: real;: real;p<>0 then:=h[k]/koef;:=( f(k)*splain(0,p,k) + f(k)*splain(l[k],p,k) )/2;i:=1 to n[k]*koef-1 do int0:=int0 + f(k)*splain(i*hh,p,k);:=int0*hh;;p=0 then:=0;:=0;k:=1 to 3 do:=h[k]/koef;:=int0 +(f(k)*splain(0,p,k) + f(k)*splain(l[k],p,k))/2;i:=1 to n[k]*koef-1 do int0:=int0 + f(k)*splain(i*hh,p,k);:=int0*hh;:=int+int0;;:=int;;:=int0;;
// составление матрицыsost_sist;, j, nn: integer;: array [1..100] of real;:=n[1]+n[2]+n[3]-2;i:=1 to nn doj:=1 to nn do matr[i,j]:=0;(matrix,matrix.txt);(matrix);(matrix,koef=);(matrix,inttostr(koef));(matrix,);[1,1]:=skal_pr(0,0,0);i:=2 to n[1] doj:=2 to n[1] do if abs(i-j)<2 then matr[i,j]:=skal_pr(i-1,j-1,1);;i:=1 to n[2]-1 doj:=1 to n[2]-1 do if abs(i-j)<2 then matr[i+n[1],j+n[1]]:=skal_pr(i-1,j-1,2);;i:=1 to n[3]-1 doj:=1 to n[3]-1 do if abs(i-j)<2 then matr[i+n[1]+n[2]-1,j+n[1]+n[2]-1]:=skal_pr(i-1,j-1,3);;[1,2]:=skal_pr(0,1,1);[1,n[1]+1]:=skal_pr(0,1,2);[1,n[1]+n[2]]:=skal_pr(0,1,3);[2,1]:=matr[1,2];[n[1]+1,1]:=matr[1,n[1]+1];[n[1]+n[2],1]:=matr[1,n[1]+n[2]];i:=1 to nn doj:=1 to nn-1 do write(matrix,matr[i,j]:10:4);(matrix,matr[i,nn]:10:4);;(matrix);(pravch,pravch.txt);(pravch);(prav_ch_int,prav_ch_tolko_int.txt);(prav_ch_int);:=1; // j - номер струныi:=0 to n[j]-1 do(prav_ch_int,integral(i,j):7:4);_ch[i+1]:=integral(i,j);(pravch,i, ,pr_ch[i+1]:7:4);;(prav_ch_int,);(pravch,);:=2; // j - номер струныi:=1 to n[j]-1 do(prav_ch_int,integral(i,j):7:4);_ch[i+n[1]]:=integral(i,j);(pravch,i, ,pr_ch[i+n[1]]:7:4);;(prav_ch_int,);(pravch,);:=3; // j - номер струныi:=1 to n[j]-1 do(prav_ch_int,integral(i,j):7:4);_ch[i+n[1]+n[2]-1]:=integral(i,j);(pravch,i, ,pr_ch[i+n[1]+n[2]-1]:7:4);;(prav_ch_int,);(pravch,);(pravch);(prav_ch_int);;resh_sist; // решение системы, j, k, nn: integer;, b, c, d, e, v, w, y: array [1..100] of real;, vec2, vec3: textfile;gauss;, j: integer;: real;i:=1 to n[1]-2 do[i]:=c[i]/b[i];[i]:=d[i]/b[i];[i]:=e[i]/b[i];[i]:=y[i]/b[i];[i]:=1;[i+1]:=b[i+1]-c[i]*a[i];[i+1]:=d[i+1]-d[i]*a[i];[i+1]:=e[i+1]-e[i]*a[i];[i+1]:=y[i+1]-y[i]*a[i];[i]:=0;[i+1]:=v[i+1]-c[i]*v[i];[n[1]+1]:=b[n[1]+1]-d[i]*v[i];[n[1]+1]:=e[n[1]+1]-e[i]*v[i];[n[1]+1]:=y[n[1]+1]-y[i]*v[i];[i]:=0;[i+1]:=w[i+1]-c[i]*w[i];[n[1]+1]:=w[n[1]+1]-d[i]*w[i];[n[1]+n[2]]:=b[n[1]+n[2]]-e[i]*w[i];[n[1]+n[2]]:=y[n[1]+n[2]]-y[i]*w[i];[i]:=0;;:=n[1]-1;[i]:=c[i]/b[i];[i]:=d[i]/b[i];[i]:=e[i]/b[i];[i]:=y[i]/b[i];[i]:=1;[i+1]:=b[i+1]-c[i]*a[i];[i+1]:=c[i+1]-d[i]*a[i];[i+1]:=e[i+1]-e[i]*a[i];[i+1]:=y[i+1]-y[i]*a[i];[i]:=0;[i+1]:=a[i+1]-c[i]*v[i];[i+2]:=b[i+2]-d[i]*v[i];[i+2]:=e[i+2]-e[i]*v[i];[i+2]:=y[i+2]-y[i]*v[i];[i]:=0;[i+1]:=w[i+1]-c[i]*w[i];[i+2]:=w[i+2]-d[i]*w[i];[n[1]+n[2]]:=b[n[1]+n[2]]-e[i]*w[i];[n[1]+n[2]]:=y[n[1]+n[2]]-y[i]*w[i];[i]:=0;i:=n[1] to n[1]+n[2]-3 do[i]:=c[i]/b[i];[i]:=e[i]/b[i];[i]:=y[i]/b[i];[i]:=1;[i+1]:=b[i+1]-c[i]*a[i];[i+1]:=e[i+1]-e[i]*a[i];[i+1]:=y[i+1]-y[i]*a[i];[i]:=0;[i+1]:=w[i+1]-c[i]*w[i];[n[1]+n[2]]:=b[n[1]+n[2]]-e[i]*w[i];[n[1]+n[2]]:=y[n[1]+n[2]]-y[i]*w[i];[i]:=0;;:=n[1]+n[2]-2;[i]:=c[i]/b[i];[i]:=e[i]/b[i];[i]:=y[i]/b[i];[i]:=1;[i+1]:=b[i+1]-c[i]*a[i];[i+1]:=e[i+1]-e[i]*a[i];[i+1]:=y[i+1]-y[i]*a[i];[i]:=0;[i+1]:=a[i+1]-b[i+1]*w[i];[n[1]+n[2]]:=b[n[1]+n[2]]-c[i]*w[i];[n[1]+n[2]]:=y[n[1]+n[2]]-y[i]*w[i];[i]:=0;i:=n[1]+n[2]-1 to n[1]+n[2]+n[3]-3 do[i]:=c[i]/b[i];[i]:=y[i]/b[i];[i]:=1;[i+1]:=b[i+1]-c[i]*a[i];[i+1]:=y[i+1]-y[i]*a[i];[i]:=0;;[nn]:=y[nn]/b[nn];[nn]:=1;;obratno;: integer;i:=1 to nn do cf[i]:=0;[nn]:=y[nn];i:=nn-1 downto n[1]+n[2]-2 do cf[i]:=y[i]-c[i]*cf[i+1];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];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];;print_vect(vectors: string);, nn: integer;: textfile;: string;:=n[1]+n[2]+n[3]-2;:=vectors+.txt;(vec,fname);(vec);(vec,a:);i:=1 to nn-1 do writeln(vec,a[i]:7:4);(vec,b:);i:=1 to nn do writeln(vec,b[i]:7:4);(vec,c:);i:=1 to nn-1 do writeln(vec,c[i]:7:4);(vec,d:);i:=1 to n[1]-1 do writeln(vec,d[i]:7:4);(vec,e:);i:=1 to n[1]+n[2]-2 do writeln(vec,e[i]:7:4);(vec,v:);i:=1 to n[1]-1 do writeln(vec,v[i]:7:4);(vec,w:);i:=1 to n[1]+n[2]-2 do writeln(vec,w[i]:7:4);(vec,y:);i:=1 to n[1]+n[2]+n[3]-2 do writeln(vec,y[i]:7:4);(vec,cf:);i:=1 to n[1]+n[2]+n[3]-2 do writeln(vec,cf[i]:7:4);(vec);;// resh_sist:=n[1]+n[2]+n[3]-2;[1]:=matr[1,1];[1]:=matr[1,2];[nn]:=matr[nn,nn];[nn-1]:=matr[nn,nn-1];i:=2 to nn-1 doj:=(i-1) to (i+1) doi=j then b[i]:=matr[i,j]i=(j-1) then c[i]:=matr[i,j]if j=(i-1) then a[i-1]:=matr[i,j];;i:=1 to n[1] do d[i]:=0;[1]:=matr[1,n[1]+1];i:=1 to n[1]+n[2]-1 do e[i]:=0;[1]:=matr[1,n[1]+n[2]];i:=1 to n[1] do v[i]:=0;[1]:=matr[n[1]+1,1];i:=1 to n[1]+n[2]-1 do w[i]:=0;[1]:=matr[n[1]+n[2],1];i:=1 to nn do y[i]:=pr_ch[i];_vect(vec1);;_vect(vec2);;_vect(vec3);;TForm1.Button3Click(Sender: TObject);, j: integer;: real;: real;: integer;i:=0 to n[1] do series1.AddXY(x1[i],u_toch(x1[i],1));i:=0 to n[2] do series3.AddXY(x2[i],u_toch(x2[i],2));i:=0 to n[3] do series5.AddXY(x3[i],u_toch(x3[i],3));:=2;:=h[1]/q;i:=0 to (n[1]-1)*q+1 do:=cf[1]*splain(x1[i],0,1);j:=1 to n[1]-1 do r:=r+cf[j+1]*splain(x1[0]+m*i,j,1);.AddXY(x1[0]+m*i,r);;.AddXY(x1[n[1]],u_toch(l[1],1));:=h[2]/q;i:=0 to (n[2]-1)*q+1 do:=cf[1]*splain(x2[i],0,2);j:=1 to n[2]-1 do r:=r+cf[j+n[1]]*splain(x2[0]+m*i,j,2);.AddXY(x2[0]+m*i,r);;.AddXY(x2[n[2]],u_toch(l[2],2));:=h[3]/q;i:=0 to (n[3]-1)*q+1 do:=cf[1]*splain(x3[i],0,3);j:=1 to n[3]-1 do r:=r+cf[j+n[1]+n[2]-1]*splain(x3[0]+m*i,j,3);.AddXY(x3[0]+m*i,r);;.AddXY(x3[n[3]],u_toch(l[3],3));;TForm1.Button2Click(Sender: TObject);_sist;_sist;(ok);;.