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

2023
Views:

61

Pages:

3
Author:

Amal J.

SapEuler Method:.Yn+1 = , x=0,1,2Modified Euler Methody(c) = yo +h for yo) +f(x,yy)2y(2) = you h 2 [ (xo, yo) 1ffxx / ,yi) (1)Y2 = yit hf [(xoth, yr]Q.dySolve the system of equation equation differentialdx = y-x ,ylo) for x=0.1y+nby taking h= 0.02 using Euler method.PP.8/8PSoln: We have xo=0 yo ==0.022Stz,y) = dy dx = y xytnxozox -0.02( " ++0.02=0.02 XI= y 1=y(o.ba) = yoth (f(x),yo)If1.40.02 (1-0) 1+0x, = 0.02YIF 1.02X230.02. h += 0.02 +0.02y2= y(0.04) =y,+h give [f(x),yi)]=0.04&= 1.02+ 0.02 1.02-0.021.02400If 1-02+ 0.02F1.04N, 1.03920.04 +X2=0.040.02Y2=010092totalya=y(0.06). = y2+h [f (xg,y2)]100.1= 1.0392 + 0.021.039-0.041.039+0.04=1.0392 +0.02f0.9991.079= 1.057 11 Y4=y(0.08)It y3+ h If (2), y3)]= 1.057+.0.021.057 - 0.0671.057+ 0.06!=1.057+0.020.99719.117JlY4. 1.074y5= y(x5) =.SB 1.078 +0.02 1.074-0.081.074+0.08[ 0.994 +123dg (down)5,1541.091ppp.00.07 SPEONpf 0.1