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伯格斯-费希尔 方程

(重定向自Burgers-Fisher 方程
Burgers Fisher PDE 3d Maple 图
Burgers Fisher pde Maple 动画
Burgers Fisher PDE Maple 图

伯格斯-費希爾 方程 (Burgers Fisher)非线性偏微分方程有如下形式:[1]

此偏微分方程的解为:

阿多米安近似解编辑

利用阿多米安分解法可求得Burgers-Fisher方程的在柯西问题 u(0)=sin(x) 初始条件下的级数展开近似解:[2]

pa := (-1.*tanh(x)-82360.*tanh(x)^13+73.*tanh(x)^3-1195.*tanh(x)^5+8233.*tanh(x)^7-29990.*tanh(x)^9+63510.*tanh(x)^15-26980.*tanh(x)^17+4862.*tanh(x)^19+63850.*tanh(x)^11)*t^9+(14650.*tanh(x)^13-16170.*tanh(x)^11+tanh(x)+1430.*tanh(x)^17+688.8*tanh(x)^5+10230.*tanh(x)^9-7102.*tanh(x)^15-54.67*tanh(x)^3-3672.*tanh(x)^7)*t^8+(-373.8*tanh(x)^5+1491.*tanh(x)^7-1.*tanh(x)+39.67*tanh(x)^3+3333.*tanh(x)^11+429.*tanh(x)^15-3036.*tanh(x)^9-1881.*tanh(x)^13)*t^7+(132.*tanh(x)^13+187.8*tanh(x)^5-502.*tanh(x)^11+743.5*tanh(x)^9-27.67*tanh(x)^3+tanh(x)-534.6*tanh(x)^7)*t^6+(-135.3*tanh(x)^9+161.1*tanh(x)^7-1.*tanh(x)+42.*tanh(x)^11-85.13*tanh(x)^5+18.33*tanh(x)^3)*t^5+(-37.*tanh(x)^7+33.33*tanh(x)^5+14.*tanh(x)^9-11.33*tanh(x)^3+tanh(x))*t^4+(5.*tanh(x)^7-10.33*tanh(x)^5+6.333*tanh(x)^3-1.*tanh(x))*t^3+(-3.*tanh(x)^3+tanh(x)+2.*tanh(x)^5)*t^2+(-1.*tanh(x)+tanh(x)^3)*t+tanh(x)

参考文献编辑

  1. ^ Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential p123-133 Equations Academy Press
  2. ^ Inna Shingareve Carlos Lizarraga Celaya,Solving Nonlinear Partial Differential Equations with Maple and Mathematica p230-236, Springer
  1. *谷超豪 《孤立子理论中的达布变换及其几何应用》 上海科学技术出版社
  2. *阎振亚著 《复杂非线性波的构造性理论及其应用》 科学出版社 2007年
  3. 李志斌编著 《非线性数学物理方程的行波解》 科学出版社
  4. 王东明著 《消去法及其应用》 科学出版社 2002
  5. *何青 王丽芬编著 《Maple 教程》 科学出版社 2010 ISBN 9787030177445
  6. Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential p135 Equations Academy Press
  7. Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser,1997
  8. Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
  9. Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
  10. Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
  11. Dongming Wang, Elimination Practice,Imperial College Press 2004
  12. David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004
  13. George Articolo Partial Differential Equations & Boundary Value Problems with Maple V Academic Press 1998 ISBN 9780120644759