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Values from the iteration x = cos(x) are:
x0 = 0.8, x1 = 0.696707, x2 = 0.766959, x3 = 0.720024, x4 = 0.751790, x5 = 0.730468.
a) Calculate the sequence {yn} from Aitken's ?2 method. Given that the solution of x = cos x is 0.739085133 . . . , ?nd the rations between consecutive errors in {xn} (which approach a constant A) and also in {yn} (which approach another constant, say B). Con?rm that {yn} is converging twice as fast as {xn} (i.e. that B = A2).
b) Use Steffensen's method: from x0, x1, x2 calculate y0. Then start the iteration again from x3 = y0, and from x3, x4, x5 calculate y1.
procedure of tracing a closed loop
the solution of diffusion equation by using separation of variables
Answer the following set of simultaneous equations using elimination or substitution method. a) x-y +z= 10 b) 3x+y+2z=34 c) -5x+2y-z=-14
In estimating the cost of a pile of bricks measured as 2m*15m*1.2m,tape is stretched 1% beyond the standard length if the count is 450 bricks to 1m^3 and bricks cost $530 per 1000,
Find the quadratic that interpolates f(x) = 2x 3 - x + 1 at the nodes x 0 = 0, x 1 = 2, x 2 = 3, a) by solving a set of three equations for the coefficients of p 2 (x) = a 2
Solve the initial value problem 11(t+1)dydt-7y=28t, for t>-1 with y(0)=14. Put the problem in standard form. Then find the integrating factor, ?(t)= , and finally find y(t)=
P=(Fv- ? Av3) (1-e-µ?) P is Power v is velocity of the belt ? is the density of the belt material ? = 1200 kg/m3 A is the cross sectional a
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A) Prove the following theorem by considering two distinct cases. For any integer n, n 2 + n is even. B) If x = r 2 - s 2 and y = 2rs for any integers r and s, then x 2 +
discussion
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