Differential Equations Lecture Work Solutions 311

Differential Equations Lecture Work Solutions 311 - 1. Use...

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1. Use the simple explicit method to solve the 1-D heat equation on the computational grid (fgure 59) with the boundary conditions u n 1 =2= u n 3 and initial conditions u 1 1 u 1 3 ,u 1 2 =1 . u n +1 j = u n j + r ( u n j +1 2 u n j + u n j 1 )=(1 2 r ) u n j + r ( u n j +1 + u n j 1 ) u 1 1 1 2 1 3 are known - initial condition u 2 1 2 3 are known - boundary conditions ThereFore u 2 2 =(1 2 r ) u 1 2 + r ( u 1 3 + u 1 1 ) j =2 ,n u 2 2 2 r + r (2 + 2) = 1 + 2 r So u 2 2 =1+2 r u 3 2 2 r ) u 2 2 |{z} 1+2 r + r ( u 2 3 + u 2 1 ) j u 3 2 2 r )(1 + 2 r )+ r (2 + 2) So u 3 2 =1+4 r 4 r 2 u 4 2 2 r ) u 3 2 |{z} 1+4 r 4 r 2 + r ( u 3 3 + u 3 1 ) j =3 u 4 2 2 r )(1 + 4 r 4 r 2 r (2 + 2) So u 4 2 =1+6 r
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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