Question

Numerical method no programm needed

4. Use first three fixed point iterations to find the approximated so- lution of the following equation 2-e" +22 3 starting from Io = 1 and round the result to 4 significant digit. (Answer: r* 33 = 0.2459 ) =

Answer 1

) With some initial guess to s called fixed point solution - Criven that, Fixed poềnt Iteration Method ;- toned poonto a point is called fixed point if it sales fies the equation as ogle). "The above forepela can be converted into reeceeresëve equation neti = g(ne)d, for es 0,112 ... iterative scheye. us 2-e? +82 x 5 s gox) 2-exte2 where glas 3 So, for eso, 1, 2; 3 = g(x :) niti 2 so, we get 2-exo x & Kiti 3 step-1 Let n be total number of iterations. so now first we have to find a te by using no=1 which & given.

2-62 txo niti 3 Srebs te trete e so in above equation. 2-0 Ly 4.0 + noti 3 2-é M no [os] g even 2-e't12 [e = 2.7182 ni 2-2.718 2+1 s 3 0.2818 in s 0.0939 step-2 X2 Now ering Previous value 24. we have to find qerita 2 niti 3 Subs têtute e=1 uti 3 2-0 tot 14 = 0.0939] 2-.-0934 (0.093933 [ Legnyer] 3 2- 1.098480 +0.0088172 3

0.91036 as 0-303455 Step-3 to Now, we have find ts by uning Previous value of kz Eteration a-e kita Niti 9 22 substitute Eras 2- & tx2 uzti 3 Q-222 +22 3 0.303455 + 20.303455R 3. [x2 = 0.303455 me 2-13542 +0.09208 3. .00 £37564 S 3 s 0.24585 o 5 The value of ix3ds 0.248-85 when this value is rounded off to y segnificent dorgits then [222 = 0.2459 so the solution of followeong eqelterom er 0.2459 rounded off to y significant degety.