Differensial tenglamalarni taqribiy yechimlarini aniqlash. Eyler usuli

9.1-Maple 7 dasturi
9.1-masalani Eyler usulida yechish.
> dsol1 := diff(y(x),x) = cos(y(x)/sqrt(5)) + x;

> init1 := y(1.8)=2.6;

> Digits := 20:
ans2:=dsolve({dsol1,init1},numeric,method= classical[heunform],
output=array([1.9,2.0,2.1,2.2]), stepsize=0.001);



9.1- dastur
10 DEF FNE (X,Y)=X+COS(Y/SQR (5))
20 PRINT: PRINT
30 PRINT “Birinchi tartibli differentsial tenglama ”
40 PRINT “ Y¹=F(X,Y) uchun”
50 PRINT “Koshi masalasini Eyler usulida”
60 PRINT “ taqribiy yechimini topish”
70 REM “boshlang’ich qiymat ,qadam”
72 REM “berilgan kesma yuqori chegarasi:”
80 READ X, Y, H, B
82 REM “boshlang’ich qiymat ,qadam”
84 REM “berilgan kesma yuqori chegarasi qiymatlari:”
88 DATA 1.8, 2.6, 0.1, 2.8
90 N=(B-X)/H
100 FOR I=1 TO N
110 Y=Y+H*FNE(X,Y)
120 X=X+H
130 PRINT “X (“;USING “###.###”;1:
140 PRINT “)=”;USING “###.###”;X;
150 PRINT “ F(“;USING “###.###”;I;
160 PRINT “)=”;USING “###.###”;Y
170 NEXT I
180 END
RUN
Birinchi tartibli differentsial tenglama
Y¹=F(X,Y) uchun
Koshi masalasini Eyler usulida
taqribiy yechimini topish.
X(1)= 1.900 Y(1)= 2.8197
X(2)= 2.000 Y(2)= 3.0402
X(3)= 2.100 Y(3)= 3.2611
X(4)= 2.200 Y(4)= 3.4823
X(5)= 2.300 Y(5)= 3.7037
X(6)= 2.400 Y(6)= 3.9251
X(7)= 2.500 Y(7)= 4.1468

X(1)= 2.600 Y(1)= 4.3688
X(9)= 2.700 Y(9)= 4.5914
X(10)= 2.800 Y(10)= 4.8150


9.1.1- dastur
5 REM SAVE"dIF-g.BAS",a
6 REM Differentsial teneglama yechimining grafigin