dt Consider the initial-value problem d = a + by(t) + csin(y(t)), 0 ≤ t ≤ 1 where y(0) = 1 and a, b, c> 0 are constants. Let us suppose that the solution satisfies M. Consider the approximation Yk+1 = Yk + (a + byk + csin(y(t)))h for k = 0, 1, 2, · · · N — 1, Yo = y(0), and h = . Prove that |y(1) – max ly"(t)| 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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= a + by(t) + c sin(y(t)), 0 <t <1 where
11. Consider the initial-value problem
y(0) = 1 and a, b, c > 0 are constants. Let us suppose that the solution satisfies
max |y"(t)| :
M < 0. Consider the approximation Yk+1
Yk + (a + byk +
0<t<1
c sin(y(t)))h for k = 0,1, 2, .. N – 1, yo = y(0), and h = . Prove that y(1) –
YN|<
-
M heb+c
2(b+c) *
Transcribed Image Text:= a + by(t) + c sin(y(t)), 0 <t <1 where 11. Consider the initial-value problem y(0) = 1 and a, b, c > 0 are constants. Let us suppose that the solution satisfies max |y"(t)| : M < 0. Consider the approximation Yk+1 Yk + (a + byk + 0<t<1 c sin(y(t)))h for k = 0,1, 2, .. N – 1, yo = y(0), and h = . Prove that y(1) – YN|< - M heb+c 2(b+c) *
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