 Wysłany: Czw 23:13, 31 Mar 2011 Temat postu: Double parabolic equation solution of high accurac |
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| Double parabolic equation solution of high accuracy stable difference scheme
Proposed a three-story three-diagonal implicit difference scheme, the local truncation error of order 0 (r + h + T i)), which is unconditionally stable and can catch up method. Is suggested that the local truncation error of order 0 (r + h ') to the solution of two second-order parabolic equation. A division processing in order to better and more extended to higher dimensional case, the double parabolic equation into two second-order parabolic equation: First: (7) ta-a2 a / chip I: 0 (  a corresponding initial conditions becomes:. . f () Io. . 『() Io ∈ ∈ Yue Yue 0,0,0,0, each second-order parabolic equation with high accuracy to solve the implicit difference scheme. High Accuracy Difference Scheme 2 [4] = a =, () example to show how to construct high accuracy difference scheme. Let P0 (, t), P. (+., T), P2 (a., T), P3 (, t +.), P. (Qiao +., T +.), P5 (a., T + ·), for = 1 {port 0 (p0) + port 1 (p1) + port 2 (p2) + port 3 (p3) + port 4 () + Port 5 Ⅱ (p5) + h [B0f (P0) + B. f (P.) + B2, (P2) + B3f (P3) + B. , (P.) + B5, (P5)]} symmetry 1 = port 2 port, Port 4: Port 5, B1 = B2, B4 = B5 and: aMa4MafaMa4Ma plant a plant on a 3x23t +,++( 9) ( 10) (12) have:: {port o +2 port. + Port, port 4 +2} + {port. + Port 4 a (B. +2 B. + B, +2 B.)} | Il + {m,MBT schuhe preise, +2 m. + +2 B. + B, +2 | Il + {(mouth. + A (B. + (13) + {m. + B1 A Tan, + (1-2r) B4} bundle 3x23t + {F2 (mouth, +2 + r (B , +2 B4) +0 (h) 4 Lin Pengcheng: Double parabolic equation solution accurate stable difference scheme for 453 * the {} to be zero in the line of algebraic equations: solving system of equations was: Port 0 +2 al + port 3 +2 a4 = 0ra3 +2 ra4 + B0 +2 Bl + B3 +2 B4 = 0 口 l + port 4 a B0-2Bl-B3-2B4 = 0ra3 +2 ra4 +2 B3 +4 B4 = 0ra4 + Bl-rB3 + (1 -2r) B4 = 0 口 mouth 4-12Bl l + A 12B4 = 0 port. = (a 12 + l, O) 8, + (a 12 +) outlet. = (6 +{)。+( 6 + ÷) no port 3 = (I 12 I). + (a 12 a lrO) 8. Port 4 = (6-1) 8. + (6 A ÷) no B0 = 4Bl +6 B'B,: 6B, +4 B. Order.: 1, = 02 {B. = 0, B. = 1; B. = Ji, = I get high accuracy difference schemes: to {(6 + l a a Ixun River (12 +) un 』l + ( 6 One of the 1) u ;::+( 6 + ÷) spit. + (a 12 +1,03,1 + (6 +÷)}+(6 a ÷) n + l a (12 +10 ,);。}+++: 0 Ka {c6 a ÷; a c. 2 +) J + c6 a ÷; + c6 + ÷ spit. + (a 12 +) u, n-+ (6 + ÷) ignorant.} + (+ lOf,. +1 + delete +. +1 of ,.+。)= 0 f = 0 because when the above difference scheme for the unconditionally stable difference scheme, therefore, equation (16) is unconditionally stable. |
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