AMME2000.docx - AMME2000 Zijie Zhao SID 470048317 This assignment is about how numerical work to solve the question Section 1 Taylor Series

AMME2000.docx - AMME2000 Zijie Zhao SID 470048317 This...

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AMME2000 Zijie Zhao SID: 470048317 March 18, 2018 This assignment is about how numerical work to solve the question. Section 1: Taylor Series Approximations f ( x ) = tanh ( x ) f xx = 2 tanh ( x )( tanh 2 ( x ) 1 ) 1.Find the leading error: Transfer following terms in term of Taylor series: 4
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2.Diagram of two stencils approximation
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Section 2: Heat Equation using Fourier Series The serious situation happens at the Honey Factory. A labour, waiting for help, is trapped in a vat. The shape of honey flowing equation is below: H(x ,0)=f(x)={3+9Lx if0≤x ≤L30ifL3<x ≤L(1)The governing equation for the change in height of honey once the membrane breaks is: ∂H∂t=D2H∂ x2(2)Hint: H is the height of the honey and constant D = 0.087m2/s1. Explain the behaviour of heat equation
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