homework5solns

homework5solns - Homework set 5 solutions 1 The condition...

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1. The condition of convergence on successive substitution is that the derivative |dF/dx| <1. This means that equation (2) must be used because at x=0 the derivative is 0, while for equation 1 the derivative is 2. F 1 x x = 0 = 2cos(0) = 2 F 2 x x = 0 = 2 2cos(0) = 0 (it is important that you know that ONLY equation (2) will work with this method because the condition for convergence is that the magnitude (absolute value) of the derivative must be less than 1). now to do successive substitution choose a number for x 1 and use it in the right side of equation (2) to get the new x value (x 2 ), then repeat to get x 3 until the value of x n and x n +1 is with in the convergence criteria. x1=0.5 x2 = 2*(0.5)-2*sin(0.5)-0.02 = 0.0211489228 x3 = 2*(0.0211489228)-2*sin(0.0211489228)-0.02=-0.0199968469 x4 = 2*(-0.0199968469)-2*sin(-0.0199968469)-0.02 etc. 2. Option Explicit Private x As Double, xOld As Double, tooBig As Double, crit As Double Function f(x) As Double f = 2 * x - 2 * Sin(x) - 0.02

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homework5solns - Homework set 5 solutions 1 The condition...

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