Solution bycranknicolsonequation1canbeapproximatedas

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, j1 ru i1, j1 ru i1, j (2 2r)u i, j ru i1, j (2) As r= 0.75 and x 0.1 Put r =0.75 in equation (2),we get 3u i1, j1 14u i, j1 3u i1, j1 3u i1, j 2u i, j 3u i1, j (3) Now I.C. is u(x,0) x i.e. u 0,0 0,u1,0 .1,u 2,0 .2,u 3,0 .3,u 4,0 .4,u 5,0 .5 u 6,0 .6,u 7,0 .7,u 8,0 .8,u 9,0 .9,u10,0 1.0 And B.C. is u(o, t) 0, u 0,0 u 0,1 u 0,2 u 0,3 ...................... u 0, j 0 u(1, t) 1 i.e. u10,0 u10,1 u10,2 u10,3 ........................ u10, j 1 Now for Ist time level we use C‐N scheme 3u 2 14u1 0.8 3u1 14u 2 3u 3 1.3 3u 2 14u 3 3u 4 3u 3 14u 4 2.4 3u 5 3u 4 14u 5 3.2 3u 6 3u 5 14u 6 4 3u 7 3u 6 14u 7 4.8 3u 8 3u 7 14u 8 5.6 3u 9 6.4 3u 8 14u 9 10.2 u1 u1,1 0.0949, u 2 u 2,1 0.1763, u 3 u 3,1 0.2947 u 4 u 4,1 0.3988, u 5 u 5,1 0.4997, u 6 u 6,1 0.5999 u 7 u 7,1 0.7000 , u 8 u 8,1 0.8000, u 9 u 9,1 0.9000 (i) Dufort Frankel Explicit Scheme is u i, j1 1 2r 2r u i, j1 u i1, j u i1, j) 1 2r 1 2r Put r=.75 u i, j1 1 3 u i, j1 u i1, j u i1, j (3) 5 5 For 2nd time level Put j=1 in (3) u 0,2 0,u10,2 1.000 1 3 u1,0 (u 0,1 u 2,1 ) .08578 5 5 3 1 u 2,2 u 2,0 (u1,1 u 3,1 ) .19376 5...
View Full Document

This note was uploaded on 04/07/2014 for the course MATH 545 taught by Professor Prof.ramabhargava during the Spring '14 term at Indian Institute of Technology, Roorkee.

Ask a homework question - tutors are online