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can be transformed into the fixed-point problem xỉ + až + 8 x1x3 + x1 + 8 X1 = 91(x1, x2) x2 = 92(x1, x2) 10 10 (a) Show that G = (g1, 92)' mapping D into R? has a unique fixed point in D = {X = (x1, x2)* : 0 < x; < 1.5, i = 1, 2}. (b) Apply functional iteration to approximate the solution.

can be transformed into the fixed-point problem xỉ + až + 8 x1x3 + x1 + 8 X1 = 91(x1, x2) x2 = 92(x1, x2) 10 10 (a) Show that G = (g1, 92)' mapping D into R? has a unique fixed point in D = {X = (x1, x2)* : 0 < x; < 1.5, i = 1, 2}. (b) Apply functional iteration to approximate the solution.

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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5. The nonlinear system xỉ – 10x1 + x, = -8, x1x3+ x1 – 10x2 + 8 = 0 can be transformed into the fixed-point problem xž + x3 + 8 x1x3 + x1 + 8 X1 = 91(x1, x2) x2 = 92(x1, x2) 10 10 (a) Show that G (91, 92)* mapping D into R? has a unique fixed point in D = {X = (x1, 82)' : 0 < x; < 1.5, i = 1, 2}. (b) Apply functional iteration to approximate the solution.
Transcribed Image Text:5. The nonlinear system xỉ – 10x1 + x, = -8, x1x3+ x1 – 10x2 + 8 = 0 can be transformed into the fixed-point problem xž + x3 + 8 x1x3 + x1 + 8 X1 = 91(x1, x2) x2 = 92(x1, x2) 10 10 (a) Show that G (91, 92)* mapping D into R? has a unique fixed point in D = {X = (x1, 82)' : 0 < x; < 1.5, i = 1, 2}. (b) Apply functional iteration to approximate the solution.
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