The equation axp-1Xn-k bxn-p±cXn-q° where the initial conditions are arbitrary positive real numbers, k, 1, p, q are non- negative integers and a, b, c are positive constants, is one of the difference equations whose solutions are associated with number sequences. Positive solutions of concrete Xn+1 = nE No, (1.1) Motivated by this line of investigations, here we show that the systems of differ- ence equations Xn+1 =f'(af (Pn-1)+bf (qn-2)), yn+1 =f'(af (rn-1)+bf (Sn-2)), (1.8) for n E No, where the sequences Pn, qn, In and Sn are some of the sequences xn and Yn, f : Df R is a "1 – 1" continuous function on its domain Df CR, the initial values x-j, y-j, je {0,1,2} are arbitrary real numbers and the parameters and a, b
The equation axp-1Xn-k bxn-p±cXn-q° where the initial conditions are arbitrary positive real numbers, k, 1, p, q are non- negative integers and a, b, c are positive constants, is one of the difference equations whose solutions are associated with number sequences. Positive solutions of concrete Xn+1 = nE No, (1.1) Motivated by this line of investigations, here we show that the systems of differ- ence equations Xn+1 =f'(af (Pn-1)+bf (qn-2)), yn+1 =f'(af (rn-1)+bf (Sn-2)), (1.8) for n E No, where the sequences Pn, qn, In and Sn are some of the sequences xn and Yn, f : Df R is a "1 – 1" continuous function on its domain Df CR, the initial values x-j, y-j, je {0,1,2} are arbitrary real numbers and the parameters and a, b
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,