Question

use the Euler method to solve the differential equation :

dv/dt = ve^(1+t)+0.5v

for t, between 0 and 0.2, in steps of 0.02; with the initial condition, v=1 when t=0. Compare your results to the excel analytical solution in tabular and graphical forms

Answer 1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

Initially given v(0)=1, h=0.02

For t=0.00, v=1.000000

Next v is v=1.000000+0.02*(1.00*exp(1+0.00)+0.5*1.00)
For t=0.02, v=1.064366

Next v is v=1.064366+0.02*(1.06*exp(1+0.02)+0.5*1.06)
For t=0.04, v=1.134043

Next v is v=1.134043+0.02*(1.13*exp(1+0.04)+0.5*1.13)
For t=0.06, v=1.209553

Next v is v=1.209553+0.02*(1.21*exp(1+0.06)+0.5*1.21)
For t=0.08, v=1.291473

Next v is v=1.291473+0.02*(1.29*exp(1+0.08)+0.5*1.29)
For t=0.10, v=1.380447

Next v is v=1.380447+0.02*(1.38*exp(1+0.10)+0.5*1.38)
For t=0.12, v=1.477193

Next v is v=1.477193+0.02*(1.48*exp(1+0.12)+0.5*1.48)
For t=0.14, v=1.582513

Next v is v=1.582513+0.02*(1.58*exp(1+0.14)+0.5*1.58)
For t=0.16, v=1.697301

Next v is v=1.697301+0.02*(1.70*exp(1+0.16)+0.5*1.70)
For t=0.18, v=1.822559

Next v is v=1.822559+0.02*(1.82*exp(1+0.18)+0.5*1.82)
For t=0.20, v=1.959411

Kindly revert for any queries

Thanks.