Differential Equations with Boundary Value Problems 2nd Edition Full download link at: https://testbankpack.com/p/solution-manual-fordifferential-equations-with-boundary-value-problems-2nd-edition-bypolking-isbn-0131862367-9780131862364/
Chapter 6. Numerical Methods
Section 6.1. Euler's Method 1. We have to =0, yo= 1 and f(t, y) = t + y. Thus, the first step of Euler's method is completed as follows. y=yo+(to+yo)h =14(0+1) x0.1 = 1.1 t =to +h=0+0.1 =0.1. The second step follows. y2=y +(t +yy)h=1.1 +(0.1 +1.1) x 0.1 = 1.22 h=t+h=0.I +0.1 =0.2. Continuing in this manner produces the results in the following table. k
0 1 2 3 4 5
t
k
0.0 0.1 0.2 0.3 0.4 0.5
1.0000 1.1000 1.2200 1.3620 1.5282 1.7210
f(t, yo)= ye 1.0000 1.2000 1.4200 1.6620 1.9282 2.2210
h 0.1 0.1 0.1 0.1 0.1 0.1
f(ts, yo)h 0.1000 0.1200 0.1420 0.1662 0.1928 0.2221
2. We have to =0, yo= 1 and f(t, y) = y. Thus, the first step of Euler's method is completed as follows. y =yo +yoh=1+1x0.1 = 1.l ti=to+h=0+0.1 =0.1. The second step follows. 2=y +yyh=1.1+1.1 x0.1 = 1.21
t=t +h=0.1+0.1 =0.2. Continuing in this manner produces the results in the following table. k h ye f(t, yo)= e th 0 0.0 1.0000 1.0000 0.1 1 0.1 1.1000 1.1000 0.1 2 0.2 1.2100 1.2100 0.1 3 0.3 1.3310 1.3310 0.1 4 0.4 1.4641 1.4641 0.1 5 0.5 1.6105 1.6105 0.1
f(ts, oh 0.1000 0.1100 0.1210 0.1331 0.1464 0.1611