To find v,(x=0.1) yn-1-0.1+ (0.1)2-1(0.1)" +급(01).-0.909675 To find y2(x=0.2) Expansion around x0 HW ya-1+(0.2). (-1) + 뿌 (2) + . (-2) +. (2)-0.837463 Expansion around x, y = x-y ý =1-9 y(x, = 0.1) = 0.1 -0.909675 =-0.809675 %3D (X=03) y(xo = 0.1) = 1+0.809675 = 1.809675 %3D --9 y(xo = 0.1) = -1.809675 ylu = - ylv (xo = 0.1) = +1.809675 = y, + (x,-x,,+ , + 5, + , 3! 41 = 0.909675 + 0.1.(-0.809675) + (0.1)2 (1.809675) + 21 (0.1) 뿌(-1.809675)+ (0.1) (1.809675) = 0.837462
To find v,(x=0.1) yn-1-0.1+ (0.1)2-1(0.1)" +급(01).-0.909675 To find y2(x=0.2) Expansion around x0 HW ya-1+(0.2). (-1) + 뿌 (2) + . (-2) +. (2)-0.837463 Expansion around x, y = x-y ý =1-9 y(x, = 0.1) = 0.1 -0.909675 =-0.809675 %3D (X=03) y(xo = 0.1) = 1+0.809675 = 1.809675 %3D --9 y(xo = 0.1) = -1.809675 ylu = - ylv (xo = 0.1) = +1.809675 = y, + (x,-x,,+ , + 5, + , 3! 41 = 0.909675 + 0.1.(-0.809675) + (0.1)2 (1.809675) + 21 (0.1) 뿌(-1.809675)+ (0.1) (1.809675) = 0.837462
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
Transcribed Image Text:EX: Solve = x - y y(0) = 1 from x-0 to x= 0.4 step size h-0.1
dx
Sol:
y(x, = 0) = 0-1 =-1
y(xa = 0) = 1+1 = 2
y(x) = y(xo) + x. y(xo) +yxo) + (x0) +y (xo) + E
y = x- y
ỹ =1-ý
%3D
yox)=D 1 +x(-1) + 플 (2) + 등(-2) + (2) + E
%3!
ỹ = -ỹ
ỹ(x, = 0) = -2
yl" (x, = 0) = 2
y(x) = 1-x + x? -x* +** + E
Numerical Solution Of Ordinary Differential Equation
To find y(x=0.1)
y = 1-0.1+ (0.1)2 - (0.1)3 +.(0.1)* = 0.909675
To find y2(x=0.2)
1 Expanslon around x0
HW
(0.2)*
ya= 1+(0.2). (-1) + 의.(2) + .(-2) +
ii. Expansion around x,
.(2) = 0.837463
y(x, = 0.1) = 0.1 - 0.909675 = -0.809675
y = x- y
ỹ =1-ý
F(xo = 0.1) = 1+0.809675 = 1.809675
(xo = 0.1) = -1.809675
%3D
yle = -3
yl" (xo = 0.1) = +1.809675
%3D
Y2 = y1 + (x2 - x,)9, + , + 5, + )5,
3!
4!
y2 = 0.909675 + 0.1. (-0.809675) +
21
(0.1) (1.809675) +
(0.1)
(-1.809675)+
(0.1)
(1.809675)
= 0.837462
3!
4!
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