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

2.Diagram of two stencils approximation

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=D∂2H∂ x2(2)Hint: H is the height of the honey and constant D = 0.087m2/s1. Explain the behaviour of heat equation