Metodo Runge Kutta-Grupo 4

 

\MAVL[RAINI MNBAJMN@ RNM NMYJMAJ NKNI IL@ B\RBJ FNB\@YNI IL N[^\AYLBY\[N L AMGLMAL[ÏN BAVA@ LRB\L@N S[JFLRAJMN@ IL AMGLMAL[ÏN BAVA@

 

Ijblmtl5Amg. Onratzn Dnthlraml Arpnmjbbn Busaonytn Lstuianmtls5 RJYJOJ@@J-S\B@@N-EHLAML[…………………….....> RJYJOJ@@J-S\B@@NEHLAML[…………………….....>>3; >3; [AVNR [AV NR N@NMQ N@NMQN N EN[LY FNKANM…………………………. FNKANM………………………….>1;631 >1;631 YYAYJ BJMIL, Onrbj Eumajr …………………………...>1976>862 VA@N SN@JOAMJ, Enoa` @amlr ……………………………>192

 

Oátjij [umgl Duttn Fjron umn fnoa`an il oátjijs lm `n lbunbaòm iaflrlmban` jriamnran qul amb`uyl n `js oátjijs trnplbaj y lu`lr , ijmil l` oátjij il lu`lr sarvl pnrn lbunbajmls il praolr jrilm y l` trnplbaj il slgumij jrilm.

Fjron glmlrn`

 

 @js bjlfabalmtls {ned}, {be} y {ke} bnrnbtlraznm l` oátjij [D y sl usnm lm umn tnk`n

``nonin tnk`n il Kutbhlr .

 

bjmsailrlojs umn LIJ il praolr

[lbjrinmij l` oátjij il Lu`lr

jrilm

OÁYJIJ IL [\MGL-D\YYN 5 >³ J[ILM

 

OÁYJIJ IL [\MGL-D\YYN 5 ;³ J[ILM Bjmeumtj il oátjijs glmárabjs atlrntavjs, il rlsj`ubaòm muoárabn il lbunbajmls iaflrlmban`ls5

Inin `n lbunbaòm5

ix/iy?f(x,y) ix/iy?

y(x3 )?y3

Fòrou`ns5 lstî ilfamaij pjr `n fòrou`n

ya+>?ya+(n>.d>+n;⋌d; )h Bjmstnmtls

Snrtalmij il um vn`jr amaban` Ijmil5

n> ,d>4n;,d; sjm bjmstnmtls H 5 ls l` tnonþj il pnsj

 

OÁYJIJ IL [\MGL-D\YYN 5 ;³ J[ILM Ynokaám `n bjmstnmtl 5 pnrn hn``nr `js vn`jrls mlblsatnojs `ns sagualmtls fòrou`ns

d>? f(Xa,ya)

n>?>-  n; n>?>-

d;? f(Xa+q.h, ya+q.d>.h)

q?>/;.n; q?>/;. n;

 

OÁYJIJR OÁY JIJR IL [\MGL-  D\YYN

 

OÁYJIJ IL [\MGL-D\YYN 5 ;³ J[ILM FÒ[O\@NR5

Qa+>?ya+n>.d>+n;⋌d; ) h n>?>- n; d>? f(Xa,ya) d;? f(Xa+q.h, ya+q.d>.h)

q?>/;.n;

 

OÁYJIJ IL [\MGL-D\YYN 5 ;³ J[ILM OÁYJIJ IL HL\M5

n;?>/; [llop`nznojs l` vn`jr il n; lm n> y q 5

ya+>?ya+(n>.d>+n;⋌d; )h

Lmtjmbls tlmlojs5

d>? f(xa ,ya)

ya+>?ya+h/;(d>+d; ya+>?ya+h/;(d >+d; )

d;? f(xa+h,ya+d>.h)

 

OÁYJIJ IL [\MGL-D\YYN 5 ;³ J[ILM OÁYJIJ IL [N@RYJM5

n;?;/2 [llop`nznojs l` vn`jr il n; lm n> y q 5 y nsa tlmlojs `js vn`jrls pnrn d> y d;

ya+>?ya+(n>.d>+n;⋌d; )h ya+>?ya+(>/2.d>+;/2d;; ).h ya+>?ya+(>/2.d>+;/2d

Lmtjmbls tlmlojs5

d>? f(xa,ya) d;? f(xa+2/9h,ya+2/9d>.h)

 

OÁYJIJ IL [\MGL-D\YYN 5 ;³ J[ILM OÁYJIJ IL S\MYJ OLIAJ5

n;?> [llop`nznojs l` vn`jr il n; lm n> y q 5 y nsa tlmlojs `js vn`jrls pnrn d> y d;

y

a+>

?ya+(n>.d>+n;⋌d; )h

ya+>?ya+ d;.h

Lmtjmbls tlmlojs5

d>? f(xa,ya) d;? f(xa+h/;,ya+h/;.d>)

 

[\MGL-D\YYN OÁYJIJ IL [\MGL-D\YY N 5 ;³ J[ILM-LELOS@JR

 

[\MGL-D\YYN OÁYJIJ IL [\MGL-D\YY N 5 ;³ J[ILM-LELOS@JR

 

[\MGL-D\YYN OÁYJIJ IL [\MGL-D\YY N 5 ;³ J[ILM-LELOS@JR

 

[\MGL-D\YYN OÁYJIJ IL [\MGL-D\YY N 5 ;³ J[ILM-LELOS@JR

 

OÁYJIJ IL [\MGL-D\YY N 5 ;³ J[ILM-LELOS@JR [\MGL-D\YYN

 

OÁYJIJ IL [\MGL-D\YY N 5 ;³ J[ILM-LELOS@JR [\MGL-D\YYN

 

OÁYJIJ IL [\MGL-D\YY N 5 ;³ J[ILM-LELOS@JR [\MGL-D\YYN

 

OÁYJIJ IL [\MGL-D\YY N 5 ;³ J[ILM-LELOS@JR [\MGL-D\YYN

 

[\MGL-D\YYN OÁYJIJ IL [\MGL-D\YY N 5 ;³ J[ILM-LELOS@JR

 

[\MGL-D\YYN OÁYJIJ IL [\MGL-D\YY N 5 ;³ J[ILM-LELOS@JR LM [LR\OLM5

 

[\MGL-D\YYN YL[BL[ J[ILM

 

 

  rou`ns5 [DZ2³ jrilm

 

Lelop`j5 ◊

 Nprjxaol `n sj`ubaòm il `n LIJ, bjmsailrnmij `j sagualmtl5

 

◊

 

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Np`abnmij `ns fjrou`ns 5  

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