Assignment2.docx - AMME2000 Yongkang XING 470019281 Section 1 Prepare Work 1 Boundary conditions u 0,t)=0,u 9 t)=0 Initial condition u x 0)=f(x 2 i

Assignment2.docx - AMME2000 Yongkang XING 470019281 Section...

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AMME2000 Yongkang XING 470019281 Section 1: Prepare Work 1)Boundary conditions: u(0,t)=0,u(9,t)=Initial condition: u(x,0)=f(x2)i)Define all the parameters:Initial conditions and boundary conditions: 0 ) 0 / s sii)Use separation of variables:Governing Equation: 2∂t2u(x,t)=c22∂ x2u(x,t)Assume a solution u(x,t)=F(x)G(t 2 ) iii)Solve the resulting ODE for F(x) : 0 )
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iv)Solve the resulting ODE for G(t) : :
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