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U8n-3 U8n-7 U8n-1 = U8n–3 + U8n–5 + U8n-5-U8n-7

U8n-3 U8n-7 U8n-1 = U8n–3 + U8n–5 + U8n-5-U8n-7

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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Solving the determine green in the same way of the determine red

U8n-3'U8n-7 U8n-1 = U8n-3 + U8n–5 + U8n-5-U8n-7
Transcribed Image Text:U8n-3'U8n-7 U8n-1 = U8n-3 + U8n–5 + U8n-5-U8n-7
e2n cn U8n-5 = an-1(c – e)"(a – c)"' U8n-4 = br-1(d – f)"(b – d)n' cn+1e2n U8n-3 = а" (а — с)"(с — е)п' dn+1 f2n b" (b – d)" (d – f)r' e2n+1 cn U8n-2 = U8n-1 = an а" (а — с)" (с — е)" fan+1dn b (b – d)"(d – f)n' cn+1e2n+1 U8n U8n+1 = а" (с— е)" (а — с)т+1° dn+1 f2n+1 b* (d – f)*(b – d)n+1* U8n+2 = This work aims to investigate the equilibria, local stability, global attractivity and the exact solutions of the following difference equations Bun-1un-5 Un+1 = aun-1+ n = 0,1,..., (1) Yun-3 - bun-5 Bun-1un-5 Un+1 = aun-1 n = 0,1, ..., (2) Yun-3 + dun-5 where the coefficients a, B, , and 6 are positive real numbers and the initial con- ditions ui for all i = -5,-4, ..., 0, are arbitrary non-zero real numbers. We also present the numerical solutions via some 2D graphs. 2. ON THE EQUATION un+1 = aun-1 + Bun-1ün-s yun-3-6un-s This section is devoted to study the qualitative behaviors of Eq. (1). The equilibrium point of Eq. (1) is given by Un-1Un-5 Un+1 = Un-1 + n = 0, 1, .., (10) Un-3 - Un-5 d" f2n-2 -1(b – d)n-1(d – f)n-1' e2n-1cn-1 U8n-10 = bn- U8n-9 an-1(a – c)*-1(c – e)a-1' f2n-1an-1 bn-1(b – d)n-1(d – f)"-1' c"e2n-1 U8n-8 = U8n-7 an-1(c – e)n-1(a –- c)n' d" f2n-1 b2-1(d- f)n-1(b – d) * U8n-6 = Moreover, Eq. (10) gives U8n-3u8n-7 U8n-1 = U8n-3 + U8n-5 - U8n-7 cn+1e2n a" (a-c)" (c-e)" e2n cn a"-(c-e)"(a-c)" c"e2n c"2n-1 cn+le2n (с-е)п-1 (а—с)" a а" (а — с)" (с — е)" c"e2n-1 an-1(c-e)"-1(a-c)" cn+le2n a" (a – c)"(c – e) a"(c – e)n-1(a – e)" (1+ e) cn+le2n c"e2n a" (a – c)" (c – e)" a" (c – e)-1(a – c)" c"e2n+1 a" (a – c)"(c – e)"
Transcribed Image Text:e2n cn U8n-5 = an-1(c – e)"(a – c)"' U8n-4 = br-1(d – f)"(b – d)n' cn+1e2n U8n-3 = а" (а — с)"(с — е)п' dn+1 f2n b" (b – d)" (d – f)r' e2n+1 cn U8n-2 = U8n-1 = an а" (а — с)" (с — е)" fan+1dn b (b – d)"(d – f)n' cn+1e2n+1 U8n U8n+1 = а" (с— е)" (а — с)т+1° dn+1 f2n+1 b* (d – f)*(b – d)n+1* U8n+2 = This work aims to investigate the equilibria, local stability, global attractivity and the exact solutions of the following difference equations Bun-1un-5 Un+1 = aun-1+ n = 0,1,..., (1) Yun-3 - bun-5 Bun-1un-5 Un+1 = aun-1 n = 0,1, ..., (2) Yun-3 + dun-5 where the coefficients a, B, , and 6 are positive real numbers and the initial con- ditions ui for all i = -5,-4, ..., 0, are arbitrary non-zero real numbers. We also present the numerical solutions via some 2D graphs. 2. ON THE EQUATION un+1 = aun-1 + Bun-1ün-s yun-3-6un-s This section is devoted to study the qualitative behaviors of Eq. (1). The equilibrium point of Eq. (1) is given by Un-1Un-5 Un+1 = Un-1 + n = 0, 1, .., (10) Un-3 - Un-5 d" f2n-2 -1(b – d)n-1(d – f)n-1' e2n-1cn-1 U8n-10 = bn- U8n-9 an-1(a – c)*-1(c – e)a-1' f2n-1an-1 bn-1(b – d)n-1(d – f)"-1' c"e2n-1 U8n-8 = U8n-7 an-1(c – e)n-1(a –- c)n' d" f2n-1 b2-1(d- f)n-1(b – d) * U8n-6 = Moreover, Eq. (10) gives U8n-3u8n-7 U8n-1 = U8n-3 + U8n-5 - U8n-7 cn+1e2n a" (a-c)" (c-e)" e2n cn a"-(c-e)"(a-c)" c"e2n c"2n-1 cn+le2n (с-е)п-1 (а—с)" a а" (а — с)" (с — е)" c"e2n-1 an-1(c-e)"-1(a-c)" cn+le2n a" (a – c)"(c – e) a"(c – e)n-1(a – e)" (1+ e) cn+le2n c"e2n a" (a – c)" (c – e)" a" (c – e)-1(a – c)" c"e2n+1 a" (a – c)"(c – e)"
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