数学季刊 ›› 2012, Vol. 27 ›› Issue (2): 238-245.

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非线性分数次边值问题改进的ADM解法

  

  1. Undergraduate College, Shangqiu Institute of Technology

  • 收稿日期:2010-09-03 出版日期:2012-06-30 发布日期:2023-03-29
  • 作者简介:WANG Jie(1983-), female, native of Luoyang, Henan, an assistant of Shangqiu Institute of Technology, M.S.D., engages in nonlinear functional analysis.

The Modified Adomian Decomposition Method for Nonlinear Fractional Boundary Value Problems

  1. Undergraduate College, Shangqiu Institute of Technology

  • Received:2010-09-03 Online:2012-06-30 Published:2023-03-29
  • About author:WANG Jie(1983-), female, native of Luoyang, Henan, an assistant of Shangqiu Institute of Technology, M.S.D., engages in nonlinear functional analysis.

摘要: We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem {D(α0) + u(x) = f(x, u(x)), 0 < x < 1, 3 < α≤ 4 u(0) = α0, u’’ (0) = α2 u(1) = β0, u’’(1) = β2} (1) where D(0α)+u is Caputo fractional derivative and α0, α2, β0, β2 is not zero at all, and f:[0,1]×R→ R is continuous. The calculated numerical results show reliability and efficiency of the algorithm given. The numerical procedure is tested on linear and nonlinear problems. 

关键词: Caputo fractional derivative, Adomian decomposition method, differential equations

Abstract: We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem {D(α0) + u(x) = f(x, u(x)), 0 < x < 1, 3 < α≤ 4 u(0) = α0, u’’ (0) = α2 u(1) = β0, u’’(1) = β2} (1) where D(0α)+u is Caputo fractional derivative and α0, α2, β0, β2 is not zero at all, and f:[0,1]×R→ R is continuous. The calculated numerical results show reliability and efficiency of the algorithm given. The numerical procedure is tested on linear and nonlinear problems. 


Key words: Caputo fractional derivative, Adomian decomposition method, differential equations

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