oddiy differensial tenglamalar

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4-mavzu. birinchi tartibli oddiy differensial tenglamalarni taqriban yechish. oddiy differensial tenglamalar uchun koshi masalasini qo‘yilishi. birinchi tartibli oddiy differensial tenglamalarni taqriban yechishning metodlari. 1-misol. ketma – ket yaqinlashish usuli bilan (pikar usuli) differentsial tenglamaning x=0 da y=1 shartni qanoatlantiruvchi xususiy echimi topilsin. yechish. bundan x=0 da y=1 ekanligini hisobga olsak, (110) ga asosan, (111) ga asosan, y3 va y4 ni hisoblaymiz: berilgan tenglamaning aniq echimi: bundan ko`rinadigan taqribiy echimlar y3 va y4 aniq echimdan faqat oxirgi hadlari bilan farq qiladi pikar usuli bo’yicha taqribiy analitik yechimni olish algoritmi mathcad sodda bajariladi u quyida korsatilgan oxirgi ikki qator nushasini olib keyinda bir necha marta qo’yilishi bilan ketma-ket yechimga yaginlashib boriladi. boshlang’ich shartni y(1)=2 deb olsak vaunga mos 1-qatorni o’zgartirsak image4.wmf oleobject4.bin image5.wmf oleobject5.bin image6.wmf oleobject6.bin image7.wmf oleobject7.bin image8.wmf oleobject8.bin image9.png image10.png image11.png image12.png image1.wmf oleobject1.bin image2.wmf oleobject2.bin image3.wmf oleobject3.bin 2 1 ) 1 ( 1 2 0 1 x x dx …
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d) yo) 2- beng) + 42- de09g + 27 qq = yo + ag cd) vo 2- bing) +44 6.0069 + 4.2 + sat yo = 90 + agc) vf 24 1deing) 4 4x4 6.0000) 44x + zaha ba? sig) press f1 for help. num) crpe y x dx dy y + = = ' y x dx dy + = ò + + = x dx y x y 0 ) ( 1

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4-mavzu. birinchi tartibli oddiy differensial tenglamalarni taqriban yechish. oddiy differensial tenglamalar uchun koshi masalasini qo‘yilishi. birinchi tartibli oddiy differensial tenglamalarni taqriban yechishning metodlari. 1-misol. ketma – ket yaqinlashish usuli bilan (pikar usuli) differentsial tenglamaning x=0 da y=1 shartni qanoatlantiruvchi xususiy echimi topilsin. yechish. bundan x=0 da y=1 ekanligini hisobga olsak, (110) ga asosan, (111) ga asosan, y3 va y4 ni hisoblaymiz: berilgan tenglamaning aniq echimi: bundan ko`rinadigan taqribiy echimlar y3 va y4 aniq echimdan faqat oxirgi hadlari bilan farq qiladi pikar usuli bo’yicha taqribiy analitik yechimni olish algoritmi mathcad sodda bajariladi u quyida korsatilgan oxirgi ikki qator nushasini olib keyinda bir necha marta qo’yilishi...

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