KKKQ 3013 PENGIRAAN BERANGKA

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KKKQ 3013PENGIRAAN BERANGKA

• Week 4 Systems of Nonlinear Equations
• 31 July 2007
• 8.00 am 9.00 am

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Topics
?? Introduction ?? Graphical Methods ?? Close
Methods ?? Open Methods ?? Polynomial Roots ??
System of Multivariable Equations
?
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Open Method 1 Newton-Raphson
Derivative defines gradient
Therefore,
Repeat ..
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Open Method 1 Newton-Raphson
In general,
..(1)
Iterate/repeat until xi1 xi lt e
(an appropriate error requirement)
Need only 1 initial guess (i.e x0) !
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Open Method 2 Secant Method
Similar concept per Newton-Raphson, but gradient
is estimated from its basic definition
Need 2 initial guess or points !!
Therefore, substituting into equation (1)
previously
to
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Tutorial Example 1
Determine the intersection of the following two
equations g(s) s6 h(s) s 1 using
the secant method assumming initial values 1.0
1.05.
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Tutorial Example 1
Intersection of two equations means at a
particular s, both g(s) and h(s) have the same
value i.e. g(s) h(s) s6 s 1
..(1) Hence, need to find s which satisfies
equation (1). Satisfying equation (1) is similar
to solving s6 s 1 0
f(s)
Therefore, need to find root of non-linear
equation f(s).
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Tutorial Example 1
If we plot f(s)
f(s)
f(s) s6-s-1
s
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Tutorial Example 1