Question

using eulers method solve the equation dy/dx=x+y y(0)=1 for x = 0.0,0.2,1.0.compare it with analytical solution?​

Answer 1

Step-by-step explanation:

1

y1 = y0 + h f(x0, y0) = 1.0 + 0.1*0.0/1.0 = 1.00

y2 = y1 + h f(x1, y1) = 1.0 + 0.1*0.1/1.0 = 1.01

y3 = y2 + h f(x2, y2) = 1.01 + 0.1*0.2/1.01 = 1.0298

y4 = y3 + h f(x3, y3) = 1.0298 + 0.1*0.3/1.0298 = 1.0589

y5 = y4 + h f(x4, y4) = 1.0589 + 0.1*0.4/1.0589 = 1.0967

y6 = y5 + h f(x5, y5) = 1.0967 + 0.1*0.5/1.0967 = 1.1423

y7 = y6 + h f(x6, y6) = 1.1423 + 0.1*0.6/1.1423 = 1.1948

y8 = y7 + h f(x7, y7) = 1.1948 + 0.1*0.7/1.1948 = 1.2534

y9 = y8 + h f(x8, y8) = 1.2534 + 0.1*0.8/1.2534 = 1.3172

y10 = y9 + h f(x9, y9) = 1.3172 + 0.1*0.9/1.3172 = 1.3855

with h = 0.2

y1 = y0 + h f(x0, y0) = 1.0 + 0.2*0.0/1.0 = 1.0

y2 = y1 + h f(x1, y1) = 1.0 + 0.2*0.2/1.0 = 1.0400

y3 = y2 + h f(x2, y2) = 1.0400 + 0.2*0.4/1.0400 = 1.1169

y4 = y3 + h f(x3, y3) = 1.1169 + 0.2*0.6/1.1169 = 1.2243

y5 = y4 + h f(x4, y4) = 1.2243 + 0.2*0.8/1.2243 = 1.3550

comparision may done by u.. if it helps msrk as brainliedy☹