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f2n dm bn-1 (d – f)"(b – d)"' cn+1e2n U8n-4 U8n-3 a" (а — с)" (с — е)п' dn+1 f2n b" (b – d)"(d – f)n ' e2n+1cn U8n-2 = U8n-1 a" (а — с)"(с — е)" f2n+ld" br (b – d)"(d – f)n’ cn+1 2n+1 a"(c – e)"(a – c)n+1? dn+1 f2n+1 b" (d – f)"(b – d)n+1* - u8n U8n+1 U8n+2 - - is work aims to investigate the equilibria, local stability, global attractivity he exact solutions of the following difference equations Bun-1un-5 Yun-3 - bun-s' n= 0,1,.., Un+1 = aun-1 + (1) Bun-1un-s Yun-3 + dun-s e the coefficients a, B, y, and 6 are positive real numbers and the initial con- Un+1 = aun-1 n = 0,1,.., (2)

f2n dm bn-1 (d – f)"(b – d)"' cn+1e2n U8n-4 U8n-3 a" (а — с)" (с — е)п' dn+1 f2n b" (b – d)"(d – f)n ' e2n+1cn U8n-2 = U8n-1 a" (а — с)"(с — е)" f2n+ld" br (b – d)"(d – f)n’ cn+1 2n+1 a"(c – e)"(a – c)n+1? dn+1 f2n+1 b" (d – f)"(b – d)n+1* - u8n U8n+1 U8n+2 - - is work aims to investigate the equilibria, local stability, global attractivity he exact solutions of the following difference equations Bun-1un-5 Yun-3 - bun-s' n= 0,1,.., Un+1 = aun-1 + (1) Bun-1un-s Yun-3 + dun-s e the coefficients a, B, y, and 6 are positive real numbers and the initial con- Un+1 = aun-1 n = 0,1,.., (2)

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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e2n cn U8n-5 = an-1(c – e)"(a – c)n' U8n-4 = bn-1(d – f)"(b– d)"' cn+1 e2n U8n-3 = a" (a – c)"(c – e)n' dn+1 f2n b" (b – d)" (d – f)n ' e2n+1cn U8n-2 = U8n-1 = a" (а — с)" (с — е)п' f2n+1d" b" (b – d)"(d – f)n ' cn+1e2n+1 U8n = U8n+1 а" (с — е)" (а — с)m+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-14n-5 yun-3 - bun-5 Un+1 = aun-1+ n = 0,1, ..., (1) Bun-1un-5 Yun-3 + dun-5' where the coefficients a, B, y, and & are positive real numbers and the initial con- ditions u for all i = -5,-4, ..., 0, are arbitrary non-zero real numbers. We also Un+1 = aun-1 n= 0,1, ..., (2) present the numerical solutions via some 2D graphs. 2. ON THE EQUATION Un+1=aun-1+ Bun-1ün-s Yun-3-dun-5 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 br-1(b – d)n-1(d – f)n-1’ e2n-1cn-1 U8n-10 = U8n-9 = an-1(a – c)"-1(c – e)n–1' fan-1n-1 bn-1(b - U8n-8 = - d)n-1(d – f)n-1> c"e2n-1 an-1(c – e)n-1(a – c)n' d" f2n-1 b2-1(d- f)n-1(b– d)"* U8n-7 = U8n-6 = Also, Eq. (10) leads to U8n-4u8n-8 U8n-2= U8n-4 + U8n-6 U8n-8 2n-1 n-1 f2n d" br-1(d – f)"(b – d)" fand" bn-1(d-f)" (b-d)n bn-1(b-d)n-1(d-f)n-I dn f2n-1 f2n-1dn-1 bn-1(b-d)n-1(d-f)n-1 f2n d" bn-1(d - f)"(b- d)" f2n dn f2n dn b" (d – f)"(b– d)n-1 | 1 b" (d – f)"(b– d)n (° f2n an+1 b" (d – f)"(b – d)" %3D (b -d)-1 ||
Transcribed Image Text:e2n cn U8n-5 = an-1(c – e)"(a – c)n' U8n-4 = bn-1(d – f)"(b– d)"' cn+1 e2n U8n-3 = a" (a – c)"(c – e)n' dn+1 f2n b" (b – d)" (d – f)n ' e2n+1cn U8n-2 = U8n-1 = a" (а — с)" (с — е)п' f2n+1d" b" (b – d)"(d – f)n ' cn+1e2n+1 U8n = U8n+1 а" (с — е)" (а — с)m+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-14n-5 yun-3 - bun-5 Un+1 = aun-1+ n = 0,1, ..., (1) Bun-1un-5 Yun-3 + dun-5' where the coefficients a, B, y, and & are positive real numbers and the initial con- ditions u for all i = -5,-4, ..., 0, are arbitrary non-zero real numbers. We also Un+1 = aun-1 n= 0,1, ..., (2) present the numerical solutions via some 2D graphs. 2. ON THE EQUATION Un+1=aun-1+ Bun-1ün-s Yun-3-dun-5 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 br-1(b – d)n-1(d – f)n-1’ e2n-1cn-1 U8n-10 = U8n-9 = an-1(a – c)"-1(c – e)n–1' fan-1n-1 bn-1(b - U8n-8 = - d)n-1(d – f)n-1> c"e2n-1 an-1(c – e)n-1(a – c)n' d" f2n-1 b2-1(d- f)n-1(b– d)"* U8n-7 = U8n-6 = Also, Eq. (10) leads to U8n-4u8n-8 U8n-2= U8n-4 + U8n-6 U8n-8 2n-1 n-1 f2n d" br-1(d – f)"(b – d)" fand" bn-1(d-f)" (b-d)n bn-1(b-d)n-1(d-f)n-I dn f2n-1 f2n-1dn-1 bn-1(b-d)n-1(d-f)n-1 f2n d" bn-1(d - f)"(b- d)" f2n dn f2n dn b" (d – f)"(b– d)n-1 | 1 b" (d – f)"(b– d)n (° f2n an+1 b" (d – f)"(b – d)" %3D (b -d)-1 ||
U8n-4 U8n-8 U8n-2 = U8n-4 + U8n-6 + U8n-8 U8n-6
Transcribed Image Text:U8n-4 U8n-8 U8n-2 = U8n-4 + U8n-6 + U8n-8 U8n-6
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