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Material Type: Assignment; Professor: Datta; Class: Numerical Analysis; Subject: MATHEMATICAL SCIENCES; University: Northern Illinois University; Term: Spring 2009;
Typology: Assignments
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y′^ = − 6 xy, y(0) = 7
from x = 0 to x = 1, with h = 0.25.
(b) Solve the above equation at x = 1 using Euler’s Method.
(c) Compare the bound obtained in (a) with the actual error obtained from (b). (Exact solution is y(x) = 7e−^3 x
2 ).
y(0) 1 = y 0 + hf (t 0 , y 0 )
y( i+1k) = yi + h 2 [f (ti, yi) + f (ti+1, y i(+1k− 1)], k = 1, 2 , · · ·
Apply this formula to obtain an approximation of y(0.2) of the IVP: y′^ = t − (^1) y , y(0) = 1, h = 0.1 with four digits accuracy.
y′^ = −y^2
y(1) = 1
and h = 0. 1
Apply Four-Step Adams-Bashforth formula to compute y(1.4), y(1.5) and y(1.6). Tabulate the results with approximate and exact values and errors. (Exact solution: y(t) = (^1) t )
