we use an inexpensive(explicit)method. Thus avoiding the need to solve ystem o equ For instance 20+ }2=1,f={f} Here, we use the super indec r to denote iteration(or time level). u will denote the solution vector. An appro imation to u at iteration r will be denoted by l' SLIDE 7 2 possible, i.e.(At=h2/2) h2 1+12f) 2.1.2 Matrix form SLIDE 8 A=D-L-U L: Lower triangl triangular (D-L-Uu=f Iterative method (L+Uu+ D-(L +U)u+D- f D-(D-A)ur+ (I-D-1A)➙✞➛✢➜➞➝s➟❭➠ ➡▼➢➐➤✌➢✎➥✐➦✎➧ ➨✞➩➨◗➫✿➭ ➩ ➯◆➯➳➲➸➵ ➺➧✏➻◗➤❽➧④➼✎➽➸➾✐➽✤➧☞➚❨➪✞➧❙➽➶➤✌➾✐➦✎➧➘➹q➧❙➚✝➪➶➥❴➾➌➴☞➾❴➷⑤➬➐➮➐➧❙➷✌➱✤➢❨✃❶❐❮❒❅❰❨Ï✝Ð✿Ñ✘Ò❱Ó✘Ô✣Õ❲Ô➞Ö✢×➸Øq❰✤Ù❘Ö✞Ù⑤Ù⑤Õ⑥ØÚÓ❭Ð❙Ó❲ÛÜÒ❲Ù➎Ñ ÛÜÔ➞Ö❅Ù✟Ñ✘ÝÞÐ✁ß❱Ð⑤ØÚÙ❙àáÓ❽â➒Ù✟ã❙Ï➶Ñ❲Ø→Ô✣Ó❲Ö➶Ð❙ä å✤➢⑦æ❝➾❴➽◗➤☛➷⑤➼✘➽➶➴❙➧✎çéè➩✞ê✟ë▼ì í î è➩ê í ï ➫ ➭ è➩ê íë▼ì î➘ð è➩ê í ➲ è➩ê íqñ ì ò➶ó ➲ ➵è í ô ➭öõ è➩ í✓÷❱øí❴ù ì❱úüû❭➭ýõ ➵èíÚ÷❑øí✐ù ì þ✒Ù❙Ý✌Ù☞ÿ✁￾❇ÙÞÏ✝Ð❙Ù Øq❰✤Ù Ð✁Ï✄✂✤Ù❙Ý➳Ô➞Ö❅Õ✎Ù✆☎✞✝✾ØÚÓ➐Õ✎Ù❙Ö✞Ó❲ØÚÙ✠Ô➞ØÚÙ☞Ý✌Ñ✘Ø➅Ô✣Ó✘Ö✠✟ÚÓ✘Ý Ø→Ô➞à✄Ù✠Û❴Ù☞Ò❲Ù❙Û✡✎ä ô ￾✴Ô➞Û➞Û❊Õ✎Ù❙Ö✞Ó❲ØÚÙ Øq❰✤Ù Ð❙Ó❲ÛÜÏ❨Ø→Ô✣Ó❲Ö✿Ò❲Ù☞☛☞ØÚÓ❲Ý❙ä✍✌ Ö④Ñ✆✂✎✂✞Ý✌Ó✏☎✎Ô➞à✄Ñ❲Ø→Ô✣Ó❲Ö➎Ø✓Ó ô Ñ❲Ø✴Ô➞ØÚÙ❙Ý✌Ñ❲Ø→Ô✣Ó❲Ö✑✝✒￾✴Ô➞Û➞Û✔✓⑤Ù✪Õ✎Ù❙Ö✞Ó❲ØÚÙ⑤Õ✕✓☞ß ô ê ä ô ê✌ë▼ì ➭ ô ê ➲ ï ➫ ➹ û î✠✖ô ê ➬ ➭ ➹✘✗ î ï ➫✖➬ ô ê ➲ ï ➫û✚✙ ➙✞➛✢➜➞➝s➟✜✛ ✢➷⑤➼✤✣✤➾✐➥❴➾❴➷✦✥✖✃❨➾➌➴✁➷⑤➼❲➷✟➧◆➤✹➷✟➱➶➼❲➷ ï ➫★✧ òó ð ➡✹➱✝➻➶➤◆ç ➺➧✠➷✟➼✪✩✎➧ ï ➫ ➼⑦➤✹➥✐➼✎æ✬✫⑦➧✠➼⑦➤✹➪◗➢✢➤✌➤✌➾✭✣✤➥❴➧⑦ç❨➾➅❐ ➧✎❐✳➹ï ➫ ➭ òó✄✮ ð ➬✁❐ ô ê✌ë❤ì ➭✰✯✗ î òó ð ✖✲✱✴✳ô ê ➲ òó ð û ✵ è➩ê✌ë▼ì í ➭✷✶ ð ➹ è➩ê íë❤ì ➲ è➩ê íqñ ì ➲ òó ➵è í ➬✹✸q➢✎æ✻✺ ➭ ✶ ú✏✙✼✙✼✙✾✽ ❐ ✿❁❀❃❂❄❀❅✿ ❆❈❇❊❉✼❋❍●❏■▲❑✔▼◆❋❍❖ ➙✞➛✢➜➞➝s➟◗P ✢➪✤➥✐➾❴➷ ✖ ✖ ➭❙❘ î✠❚⑥î✜❯ ❱❲❳ ❘❩❨❭❬➾✐➼✪✫✎➢✎➽◗➼✘➥ ❚ ❨❭❪➢➺➧❙æ❃➷✟æ✌➾➌➼✘➽❊✫⑦➻✤➥➌➼✘æ ❯ ❨❭❫➪➶➪◗➧◆æ❝➷✌æ✟➾✐➼✎➽❊✫✎➻➶➥✐➼✎æ ✖ ô ➭➀û ✣✞➧◆➴❙➢✎➮➐➧◆➤ ➹❘ î✠❚⑥î✜❯➬ ô ➭❢û ❴✓➷✌➧◆æ✟➼✘➷✌➾✐➦✎➧✠➮➐➧☞➷✌➱➶➢✝✃ ❘ ô ê✌ë▼ì ➭ ➹❚ ➲ ❯➬ ô ê ➲ û ➙✞➛✢➜➞➝s➟◗❵ ô ê✟ë▼ì ➭ ❘ ñ ì ➹❚ ➲ ❯➬ ô ê ➲ ❘ ñ ì û ➭ ❘ ñ ì ➹❘ î◗✖➬ ô ê ➲ ❘ ñ ì û ➭ ➹✘✗ î ❘ ñ ì ✖➬ ô ê ➲ ❘ ñ ì û ❛