{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Hs by the average of u i1 j and u i1 j u i j ie 1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: u i, j ,i.e. 1 u i1, j u i1, j 2 (4.3) Substituting relation (4.3) in equation (4.2) ,we get u i, j1 1 2r 2r u i. j1 u i1, j u i1, j (4.4) 1 2r 1 2r This scheme is called Dufort Frankel Explicit scheme. The advantage of this scheme is that inspite of it being an Explicit scheme, it has truncation error o( t) 2 o(x) 2 . But on the other hand, it requires the solution at the first time level to be determined by any other two time level scheme. For j = 2 onwards, this scheme can be applied. The computational molecule of this scheme is as shown in fig(2). u i,j+1 (j+1)th level jth level 2 r 2r u i, j u i+1,j u i‐1,j (j‐1)th level u i,j‐1 Fig (2) These schemes however have some problem with stability and compatibility which will be discussed later. Example: Solve the partial differential equation : u 2u t dx 2 Subject to ; 0 x 1, t 0 u x,0 x,u 0,t 0 ; u 1, t 1, With r 0.75, x 0.1 Obtain the solution at first time level using C-N scheme and obtain the second time level by (i) Dufort Frankel (ii) Richardson and compare the result. Solution: By Crank Nicolson, equation (1) can be approximated as ru i1, j1 (2 2r...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online