backward euler reethi

samkhyaa vishakalanathilum shaasthreeya computingilum, saadhaarana deferential samavaakyangalude parihaarathinulla ettavum adisthaana samkhyaa reethikalil onnaanu backward euler reethi (allengil inplisit euler reethi). ithu (staanderd) euler reethikk samaanamaan, pakshe ithu oru avyaktha reethiyaanennathil vyathyaasamund. backward euler reethikk krithyasamayathu oru oordaril pishakund.
vivaranam.
saadhaarana deferential samavaakyam pariganikkuka 
prarambha moolya soothravaakyam _ 2 ulla ivide function formula _ 3 umm prarambha dattaa formula _ 4 umm formula _ 5 umm ariyappedunnu; function formula _ 6 yadhaartha variable formula _ 7 neey aasrayichirikkunnu, athu anjjaathamaanu. oru samkhyaa reethi formula 9 ekadesha formula 10 ennu vilikkunna oru sequence formula 8 nirmmikkunnu, ivide formula 11 neey steppu sais ennu vilikkunnu.
backward euler reethi upayogichu ekadesha kanakkukoottalukal kanakkakkunnu
formula 14 nuu pakaram formula 13 upayogikkunna forwade reethi (forwade) euler reethiyil ninnu ithu vyathyasthamaan.
backward euler reethi oru avyaktha reethiyaanu puthiya ekadesha soothravaakyam _ 15 samavaakyathinte iruvashathum prathyakshappedunnu, athinaal reethi anjjaathamaaya soothravaakyathinu oru beejaganita samavaakyam pariharikkendathundu. karkkashamallaatha prashnangalkk, ithu nischitha-pooyint aavarthanathiloode cheyyaam
eee kramam othucherukayaanenkil (oru nischitha sahishnuthaykkullil), reethi athinte paridhi puthiya ekadesha kanakkayi edukkunnu.
formula _ 15.
pakaramaayi, beejaganita samavaakyam pariharikkunnathin oraalkk nyoottan-graafsan reethi (chila parishkkaranangal) upayogikkaam.
derivation.
formula _ 20 muthal formula _ 21 vare deferential samavaakya formula _ 1 samyojippikkunnath vilavu nalkunnu.
ippol valathuvashathulla integral valathuvashathulla deerghachathura reethi (oru deerghachathuram upayogichu) upayogichu ekadeshamaayi kanakkaakkuka
avasaanamaayi, aaa formula _ 24 upayogikkuka, athu ekadesha formula _ 25 aanennu karuthappedunnu, pinnoca euler reethiyude formula pinthudarunnu.
valathukaikk pakaram idathu kaii deerghachathura niyamam upayogikkukayaanenkil athe yukthi (staanderd) euler reethiyilekku nayikkunnu.
vishakalanam.
bigg ooo notteshan upayogichu backward euler reethiyude local trankeshan error (oru ghattathil varuthiya pishak ennu nirvachikkappedunnu) formula _ 26 aanu. oru nirddishta samaya soothravaakyathile pishak formula _ 27 aanu. athaayath eee reethikk oordar onnu undu ennaanu ithinartham. pothuve, formula _ 29 ell. tii. iii (local trankeshan error) ulla oru reethi "keey" th oordarilaanennu parayappedunnu.
1 kendreekrithamaaya 1 radiusulla diskinte sankeernna thalatthile poorakamaanu backward euler reethiyude samboornna sthirathayude pradesham, chithratthil chithreekarichirikkunnu. ithil sankeernamaaya thalatthinte muzhuvan idathu pakuthiyum ulppedunnu, ithu kadinamaaya samavaakyangalude parihaarathinu anuyojyamaakkunnu. vaasthavathil, backward euler reethi thulyamaaya ell-sthirathayullathaanu.
backward euler reethi prakaram oru vyathiriktha sthirathayulla samvidaanathinte pradesham z-playinil (0.5,0) sthithicheyyunna 0.5 vyaasamulla oru vrithamaanu.
vipuleekaranangalum parishkkaranangalum.
(forwade) euler reethiyude oru vakabhedamaanu backward euler reethi. semi-implisit euler reethiyum exponential euler reethiyumaanu mattu vakabhedangal.
kashanangalude pattika vivarikkunna oru ghattamulla oru runch-kutta reethiyaayi backward euler reethiye kaanaan kazhiyum
oru ghattamulla oru leanier multistep reethiyaayum eee reethiye kaanaan kazhiyum. adams-moulttan reethikalude kudumbatthile aadya reethiyaanithu, koodaathe pinnoca deferentiation soothravaakyangalude kudumbavum koodiyaanithu.

