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

2023
Views:

238

Pages:

5
Author:

Amal J.

Modified Euler Method (Improved EulerMethod]y,* = yo + h (f(xo,yo))gi= = yo +h 2 [f +Y2 = yit*y2 = y,1+ 2 [fix,yo +f (x2,y2Q.Using modified Falor Method, Solvenumerically dy dx s y+ 8inx, y(0)='2 =for x=0.2 by taking h=0.1)No - 0 Btflesyo=f 2pmhoox1= 0.1 ,n2=0.2y,== = yo+h (f(xo, yo))y1* = 2+h(it2.1y, * = 12+0,1[9+0]= 2.2Y1= = 2+ 2++2+2 1.7 ]22 2.210 organt = g,++Y2 * = 2.210 +0.1 [2.210 + 8in 0.1]= 2.431Y2 = gith 2 C +f(x2,ya +Y2 = 2.210 + 0.1 2.210 +sino.,2t 2.4314 Sin o.2Z / 2.4423Q.Given dy dx = ytex , yeo) =0.Find y(o.2) and y 0.4 usingmodified Euler's method h=0.2.Ansxo-o sto sareyo = ox1=0.2Copx2=0.4Fott .0+y,=yo+g,* 7 + 0+ 0.2+ity, * THE 0.2 YI= yoth +y, 0+0.2 2 1+=g,= 0.242y2 = y,y2* = 0.242+0.2 [0.242 + e 0.2]y2*= = 0.534pt.y2= = y,+ 2 +f(]0.242y2 = yr 0.2 2 [0.942,78 0.2y2 = 0.590ofat x = 0.25 given y'= = 2xy, y(o)=Using Fuler's method find y, h= 0.25 check your answer withexact Solution.Ans.no = 0yo = 1"1=0-25 , x2 = 0.5 Ynti CH[ & Syi = 'yo'+ rif(xo,yo)y,=itifexact Solution 18.0dyZ 2xydxfdy the is oflogy=2x2tc2768logyl= 4 nitelogy boilt N logx plogsoflegdOf(swearlog(Ly) x2 = lagenvisturesfoorJuly xa = C,Iof2.0 SUSin logy==lage R9 tcy= exq +Cwhen x=0, y='s we get1= etcC=O 2Hence the solution ,y=expy(o.as)(0-25)== 1.064