University:
Swansea University
Course:
MA-252 | Probability Theory
Academic year:

2023
Views:

272

Pages:

5
Author:

Amal J.

Q.using RK method, find y(o.s) forequation dy y-x , y(o)= 1.Iny+x', take h=0-2y(0:2)y1isxo= yo=1y(04)NI= 0.2, y, =x==h=K1= hf (no / yo)K1 = 0.2 [1-10] = 0.2 K2= hip (20th t; you21Ka=0.2f(0.1, 1+0.1)(ii),1.0K2= 0.2 [ 1-1-0-17 1.1+0.1(3 0.20 Sifflofif'= O. 1666Ref K3= If( noth yotkzifonly 27= 04/06/1666)2N1,5:0)0.2f b (0.1, d-0831)10=0.2[1.0833 - 0.11-0833 to:lon=0.210.98.23of& = 0.166191)8.0- Kq = 0.2f(0.2, It 0.16619)= 1,6619)= paff= =0.21 1-16619 - 0.21.16619 0-2+0-2=0.020.966191.36619= 0.14141y1= yoth [0.2+ 2(0.1666)t. 12(0.16619)TO.1414y = 1.16783Q.R.K method. Given dy y-2xSolve y for x=0.2,0.4 usingand y=' at n=0. 9xyAneno =0h=0.2yo = 1x1=0.2 KK = hf(ro, yo)= 1-2x0)[ST0.2 XI== / 0.2OK2= hf ( 20th 2 , yoth12) 21= 0.2= 0.2/ 1.1 - 1.1(ddd).0)(pludt 0.187K3z f(not all h yo-kg)if2prior0.9-P(091, lit 0.184)21-1 = 0.2 f (0.1, 1.092) How= 0.2 [ 15092 - - 2x0.11.092)= 0.1817((thop K4 hf(noth, yo+ks)= 0.2f(0.2, 1.1817)0.2 - 2x.21.1817= 0.2957 0.1686Age yoty1= 1+16 [0.94 0.1686 2 x 0 . 184 +2x 0-1817 0.1686 0.181-+= 204 =0.1833yaK1= hf(n,,yj)K2 you 2K3= yit K2) 2Kq =hf(xqth, yitks)y2= +