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Theorem 3. Every solution of Eq.(1) is bounded if a + < 1.

Theorem 3. Every solution of Eq.(1) is bounded if a + < 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Show me the steps of determine yellow and information is here step by step .(why)!!it complete

Bxn-10n-2 Xn+1 = axn-2+ п 3D 0, 1, ..., (1) YXn-1 + dxn-4
Transcribed Image Text:Bxn-10n-2 Xn+1 = axn-2+ п 3D 0, 1, ..., (1) YXn-1 + dxn-4
Theorem 3. Every solution of Eq.(1) is bounded if a + <1. Proof: Let {n}-3 be a solution of Eq.(1). It follows from Eq.(1) that (a+) - BxnTn-2 Xn+1 = axn-2 + < axn-2 + Xn-2. YXn + dxn-4 YXn Then Xn+1 < Xn-2 for all n > 0. Then the subsequences {x3n}0: {x3n+1}0; {X3n+2}0 are decreasing and so are bounded from above by M = max{x_4, x_3, X–2, X –1, X0}. n=0> n=0
Transcribed Image Text:Theorem 3. Every solution of Eq.(1) is bounded if a + <1. Proof: Let {n}-3 be a solution of Eq.(1). It follows from Eq.(1) that (a+) - BxnTn-2 Xn+1 = axn-2 + < axn-2 + Xn-2. YXn + dxn-4 YXn Then Xn+1 < Xn-2 for all n > 0. Then the subsequences {x3n}0: {x3n+1}0; {X3n+2}0 are decreasing and so are bounded from above by M = max{x_4, x_3, X–2, X –1, X0}. n=0> n=0
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