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Step 1 Given nonlinear differential equation; bxn-k Xn+1 = Axn + Bxn-k + Cxp-1 + Dxn-o + [dxn-k-exn-1 .(1)

Step 1 Given nonlinear differential equation; bxn-k Xn+1 = Axn + Bxn-k + Cxp-1 + Dxn-o + [dxn-k-exn-1 .(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 red

Step 1 Given nonlinear differential equation; bxn-k Xn+1 = Axn + Bxn-k + Cxn-1 + Dxn-o + [dxn-k-exn-1] ..... .... Step 2 Considering equation (1) for some N 2 0, bxN-k XN+1 = = AxN + BXN-k + CxN-1 + DxN-o + [dxN-k-exN-1 . .(a) for 2 < XN < 1 and b # e, given initial condition, XN-I+1, •.. , ...., XN-1, XN E 2, 1| b S XN-+1,…. , XN-k+1, •·• , XN-1, XN < 1 d applying initial condition, sa(1) + B(1) + c(1) + >(1) + (a) = XN+1 < A bxN-k XN+1 <A +B + C + D + [dxN-k-exN-1] which is named as equation (46) and can be written as XN+1 < A +B + C + D + b(1) [dxN-k-exN-1] b XN+1 <A +B + C + D+ [dxN-k-exN-1] ..(b)
Transcribed Image Text:Step 1 Given nonlinear differential equation; bxn-k Xn+1 = Axn + Bxn-k + Cxn-1 + Dxn-o + [dxn-k-exn-1] ..... .... Step 2 Considering equation (1) for some N 2 0, bxN-k XN+1 = = AxN + BXN-k + CxN-1 + DxN-o + [dxN-k-exN-1 . .(a) for 2 < XN < 1 and b # e, given initial condition, XN-I+1, •.. , ...., XN-1, XN E 2, 1| b S XN-+1,…. , XN-k+1, •·• , XN-1, XN < 1 d applying initial condition, sa(1) + B(1) + c(1) + >(1) + (a) = XN+1 < A bxN-k XN+1 <A +B + C + D + [dxN-k-exN-1] which is named as equation (46) and can be written as XN+1 < A +B + C + D + b(1) [dxN-k-exN-1] b XN+1 <A +B + C + D+ [dxN-k-exN-1] ..(b)
< XN-I+1,… d XN-k+1, XN-1, XN < 1 •.. , applying initial condition, + B(1) + c(1) + D(1) (а) —> XN+1 <A(1) + F bxN-k XN+1 <A + B +C + D + [dxN-k-exN-1 v-1] which is named as equation (46) and can be written as b(1) XN+1 <A + B + C +D + [dxy-k-exn-1] XN+1 <A + B+ C + D + [dxy-k-exN-1] ..(b) Also from initial condition, < XN-k < 1 * < XN-1 <1 d d b< dxn-k <d XN-1 < 1 = dxN-k 2 b → -XN-1 2 -1 » dxN-k exN-1 2 b – e(1) (using → dxN-k еxN-1 > b —е 1 dxN-k-exN-1 b-e above inequalities) substituting in (b), b XN+1 <A + B + C + D + b-e which is named as equation (47).
Transcribed Image Text:< XN-I+1,… d XN-k+1, XN-1, XN < 1 •.. , applying initial condition, + B(1) + c(1) + D(1) (а) —> XN+1 <A(1) + F bxN-k XN+1 <A + B +C + D + [dxN-k-exN-1 v-1] which is named as equation (46) and can be written as b(1) XN+1 <A + B + C +D + [dxy-k-exn-1] XN+1 <A + B+ C + D + [dxy-k-exN-1] ..(b) Also from initial condition, < XN-k < 1 * < XN-1 <1 d d b< dxn-k <d XN-1 < 1 = dxN-k 2 b → -XN-1 2 -1 » dxN-k exN-1 2 b – e(1) (using → dxN-k еxN-1 > b —е 1 dxN-k-exN-1 b-e above inequalities) substituting in (b), b XN+1 <A + B + C + D + b-e which is named as equation (47).
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