D:\jknuba_2025_spring\jknuba_NM\jknuba_NM_Job6_spiral.wxmx
Insert command FOR (original - jknuba_NM_Job6.wxmx)
Insert TEXT about iterations (original - jknuba_NM_Job6b.wxmx)
Insert other function about iterations (original - jknuba_NM_Job6c.wxmx)

Метод ітерацій (Method of iterations)

(%i8) kill(all);

\[\]\[\tag{%o0} \ensuremath{\mathrm{done}}\]

(%i1) Y1(x):=0.9·x;

\[\]\[\tag{%o1} \mathop{Y1}(x)\mathop{:=}0.9 x\]

(%i2) Y2(x):=−2.2·(x+1)+12;

\[\]\[\tag{%o2} \mathop{Y2}(x)\mathop{:=}\mathop{-}2.2 \left( x\mathop{+}1\right) \mathop{+}12\]

(%i3) X(n):=((n−12)/(−2.2))−1;

\[\]\[\tag{%o3} \mathop{X}(n)\mathop{:=}\frac{n\mathop{-}12}{\mathop{-}2.2}\mathop{-}1\]

(%i4) R(x):=Y1(x)−Y2(x);

\[\]\[\tag{%o4} \mathop{R}(x)\mathop{:=}\mathop{Y1}(x)\mathop{-}\mathop{Y2}(x)\]

(%i5) plot2d([Y1(x),Y2(x)],[x,0,7],
   [legend, "Y1(x):=0.9*x","Y2(x):=-2.2*(x+1)+12"],
   [style, [lines, 3,5], [lines, 3,1]]);

\[\]\[\tag{%o5} false\]

Figure 1:
Diagram
Iteration 1 i - x1[0], m - Y1[0], o -x2[0], M - Y1, N - Y2
(%i6) delta:0.1;

\[\]\[\tag{%o6} 0.1\]

(%i7) x_start:0;

\[\]\[\tag{%o7} 0\]

(%i8) x1[0]:x_start;

\[\]\[\tag{%o8} 0\]

(%i10) Y1[0]:Y1(x1[0]);x2[0]:X(Y1[0]);

\[\]\[\tag{%o9} 0\]

\[\]\[\tag{%o10} 4.454545454545454\]

(%i11) if (Y1(x2[0])−Y2(x2[0])<delta)then display("OK")else display(Y1(x2[0])−Y2(x2[0]));

\[\]\[4.009090909090909\mathop{+}-0.0\mathop{=}4.009090909090909\]

\[\]\[\tag{%o11} \ensuremath{\mathrm{done}}\]

(%i13) x2[0];Y2(x2[0]);

\[\]\[\tag{%o12} 4.454545454545454\]

\[\]\[\tag{%o13} 0.0\]

(%i14) plot2d([Y1(x),Y2(x),[discrete,[x1[0],x2[0]],[Y1(x1[0]),Y2(x2[0])]], [discrete,[x2[0]],[Y2(x2[0])]]],[x,0,7],
   [legend, "Y1(x):=0.9*x","X(n):=(n-12)/(-2.2)-1", "Iteration", "point"],
   [style, [lines, 3,5], [lines, 3,1], [lines, 2,2], [points,6,1 ]]);

\[\]\[\tag{%o14} false\]

Figure 2:
Diagram

Command FOR

i - x1[0], m - Y1[0], o -x2[0], M - Y1, N - Y2
(%i15) delta:0.01;

\[\]\[\tag{%o15} 0.01\]

(%i17) x_start:0;for i:1 thru 6 step 1 do (x1[i]:x_start,Y1[i]:Y1(x1[i]),x2[i]:X(Y1[i]),
    if (Y1(x2[i])−Y2(x2[i])<delta)then display("OK")else
    (del:Y1(x2[i])−Y2(x2[i]),display(del)),x_start:x2[i],display(x2[i]),
plot2d([Y1(x),Y2(x),[discrete,[x1[i],x2[i]],[Y1(x1[i]),Y2(x2[i])]],
            [discrete,[x2[i],x2[i]],[Y1(x2[i]),Y2(x2[i])]],
            [discrete,[x2[i]],[Y2(x2[i])]]],[x,0,7],
   [legend, "Y1(x):=0.9*x","X(n):=(n-12)/(-2.2)-1", "Iteration","Iteration_2", "point"],
   [style, [lines, 3,5], [lines, 3,1], [lines, 2,2],[lines, 5,3], [points,6,1 ]]))$

\[\]\[\tag{%o16} 0 \]\[\ensuremath{\mathrm{del}}\mathop{=}4.009090909090909 \]\[{{\ensuremath{\mathrm{x2}}}_1}\mathop{=}4.454545454545454 \]\[\mbox{}\\"OK"\mathop{=}"OK" \]\[{{\ensuremath{\mathrm{x2}}}_2}\mathop{=}2.6322314049586777 \]\[\ensuremath{\mathrm{del}}\mathop{=}0.6709429000751315 \]\[{{\ensuremath{\mathrm{x2}}}_3}\mathop{=}3.377723516153268 \]\[\mbox{}\\"OK"\mathop{=}"OK" \]\[{{\ensuremath{\mathrm{x2}}}_4}\mathop{=}3.072749470664572 \]\[\ensuremath{\mathrm{del}}\mathop{=}0.11228589856629201 \]\[{{\ensuremath{\mathrm{x2}}}_5}\mathop{=}3.197511580182675 \]\[\mbox{}\\"OK"\mathop{=}"OK" \]\[{{\ensuremath{\mathrm{x2}}}_6}\mathop{=}3.1464725353798144\]

(%i18) for i:1 thru 6 step 1 do display(x2[i]);

\[\]\[{{\ensuremath{\mathrm{x2}}}_1}\mathop{=}4.454545454545454 \]\[{{\ensuremath{\mathrm{x2}}}_2}\mathop{=}2.6322314049586777 \]\[{{\ensuremath{\mathrm{x2}}}_3}\mathop{=}3.377723516153268 \]\[{{\ensuremath{\mathrm{x2}}}_4}\mathop{=}3.072749470664572 \]\[{{\ensuremath{\mathrm{x2}}}_5}\mathop{=}3.197511580182675 \]\[{{\ensuremath{\mathrm{x2}}}_6}\mathop{=}3.1464725353798144\]

\[\]\[\tag{%o18} \ensuremath{\mathrm{done}}\]

Iteration 2
(%i20) plot2d([Y1(x),Y2(x),
        [discrete,[x1[1],x2[1]],[Y1(x1[1]),Y2(x2[1])]],
        [discrete,[x2[1],x2[1]],[Y1(x2[1]),Y2(x2[1])]],
        [discrete,[x2[1]],[Y2(x2[1])]]
    ],[x,0,7],
   [legend, "Y1(x):=0.9*x","X(n):=(n-12)/(-2.2)-1", "Iteration","Iteration_2", "point"],
   [style, [lines, 3,5], [lines, 3,1], [lines, 2,2],[lines, 5,3], [points,6,1 ]])$
Figure 3:
Diagram
(%i21) plot2d([Y1(x),Y2(x),
        [discrete,[x1[1],x2[1]],[Y1(x1[1]),Y2(x2[1])]],
        [discrete,[x2[1],x2[1]],[Y1(x2[1]),Y2(x2[1])]],
        [discrete,[x2[1]],[Y2(x2[1])]],
    [discrete,[x1[2],x2[2]],[Y1(x1[2]),Y2(x2[2])]],
        [discrete,[x2[2],x2[2]],[Y1(x2[2]),Y2(x2[2])]],
        [discrete,[x2[2]],[Y2(x2[2])]],
    [discrete,[x1[3],x2[3]],[Y1(x1[3]),Y2(x2[3])]],
        [discrete,[x2[3],x2[3]],[Y1(x2[3]),Y2(x2[3])]],
        [discrete,[x2[3]],[Y2(x2[3])]]
    ],[x,0,7],
   [legend, "Y1(x):=0.9*x","X(n):=(n-12)/(-2.2)-1", "Iteration_1","Iteration_1d", "point_1",
        "Iteration_2","Iteration_2d", "point_2",
    "Iteration_3","Iteration_3d", "point_3"],
   [style, [lines, 3,5], [lines, 3,1], [lines, 2,2],[lines, 5,3], [points,4,2 ],[lines, 2,2],[lines, 5,3], [points,4,7 ]
    ,[lines, 2,2],[lines, 5,3], [points,4,2 ]])$
(%i21) maxima_tempdir;

\[\]\[\tag{%o21} "C:/Users/y/AppData/Local/Temp"\]

Figure 4:
Diagram

Created with wxMaxima.

The source of this Maxima session can be downloaded here.