Theory and Modern Applications
From: Exact finite-difference scheme and nonstandard finite-difference scheme for coupled Burgers equation
(x,y) | t = 0.01 | t = 0.5 | t = 2 | ||||||
---|---|---|---|---|---|---|---|---|---|
First | Second | Exact | First | Second | Exact | First | Second | Exact | |
(0.1,0.1) | 0.62480 | 0.62481 | 0.62480 | 0.61522 | 0.61528 | 0.61525 | 0.58713 | 0.58718 | 0.58716 |
(0.5,0.1) | 0.59419 | 0.59421 | 0.59420 | 0.58533 | 0.58544 | 0.58540 | 0.56120 | 0.56130 | 0.56127 |
(0.9,0.1) | 0.56708 | 0.56708 | 0.56708 | 0.55979 | 0.55986 | 0.55983 | 0.54108 | 0.54114 | 0.54113 |
(0.3,0.3) | 0.62480 | 0.62481 | 0.62480 | 0.61512 | 0.61538 | 0.61525 | 0.58701 | 0.58725 | 0.58716 |
(0.7,0.3) | 0.59419 | 0.59421 | 0.59420 | 0.58522 | 0.58551 | 0.58540 | 0.56108 | 0.56136 | 0.56127 |
(0.1,0.5) | 0.65543 | 0.65544 | 0.65543 | 0.64622 | 0.64635 | 0.64628 | 0.61712 | 0.61726 | 0.61720 |
(0.5,0.5) | 0.62480 | 0.62481 | 0.62480 | 0.61503 | 0.61546 | 0.61525 | 0.58688 | 0.58734 | 0.58716 |
(0.9,0.5) | 0.59419 | 0.59421 | 0.59420 | 0.58523 | 0.58551 | 0.58540 | 0.56108 | 0.56136 | 0.56127 |
(0.3,0.7) | 0.65543 | 0.65544 | 0.65543 | 0.64612 | 0.64648 | 0.64628 | 0.61698 | 0.61739 | 0.61729 |
(0.7,0.7) | 0.62480 | 0.62481 | 0.62480 | 0.61500 | 0.61550 | 0.61525 | 0.58680 | 0.58740 | 0.58716 |
(0.1,0.9) | 0.68261 | 0.68262 | 0.68261 | 0.67478 | 0.67488 | 0.67481 | 0.64811 | 0.64823 | 0.64817 |
(0.5,0.9) | 0.65543 | 0.65544 | 0.65543 | 0.64613 | 0.64647 | 0.64628 | 0.61696 | 0.61740 | 0.61720 |
(0.9,0.9) | 0.62480 | 0.62481 | 0.62480 | 0.61512 | 0.61537 | 0.61525 | 0.58697 | 0.58728 | 0.58716 |