ON A GENERALIZED TAYLOR THEOREM: A RATIONAL PROOF OF THE VALIDITY OF THE HOMOTOPY ANALYSIS METHOD
作者： Liao Shi-jun
DOI: 10.1007/BF02439377
关键词:
摘要: A generalized Taylor series of a complex function was derived and some related theorems about its convergence region were given. The theorem can he applied to greatly enlarge regions approximation given by other traditional techniques. rigorous proof the also provides us with rational base validity new kind powerful analytic technique for nonlinear problems, namely homotopy analysis method.
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sci-hub.se 参考文章(12)
Shi-Jun Liao, A Simple Approach of Enlarging Convergence Regions of Perturbation Approximations Nonlinear Dynamics. ,vol. 19, pp. 93- 111 ,(1999) , 10.1023/A:1008373627897
George Adomian, Solving Frontier Problems of Physics: The Decomposition Method ,(1993)
Shi-jun Liao, A kind of approximate solution technique which does not depend upon small parameters — II. An application in fluid mechanics International Journal of Non-linear Mechanics. ,vol. 32, pp. 815- 822 ,(1997) , 10.1016/S0020-7462(96)00101-1
Shi-Jun Liao, An approximate solution technique not depending on small parameters: A special example International Journal of Non-linear Mechanics. ,vol. 30, pp. 371- 380 ,(1995) , 10.1016/0020-7462(94)00054-E
G Adomian, Nonlinear stochastic differential equations Journal of Mathematical Analysis and Applications. ,vol. 55, pp. 441- 452 ,(1976) , 10.1016/0022-247X(76)90174-8
Nabil T. Shawagfeh, Analytical approximate solutions for nonlinear fractional differential equations Applied Mathematics and Computation. ,vol. 131, pp. 517- 529 ,(2002) , 10.1016/S0096-3003(01)00167-9
Abdul-Majid Wazwaz, The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model Applied Mathematics and Computation. ,vol. 110, pp. 251- 264 ,(2000) , 10.1016/S0096-3003(99)00131-9
Shi-Jun Liao, An analytic approximation of the drag coefficient for the viscous flow past a sphere International Journal of Non-linear Mechanics. ,vol. 37, pp. 1- 18 ,(2002) , 10.1016/S0020-7462(00)00092-5
SHIJUN LIAO, ANTONIO CAMPO, Analytic solutions of the temperature distribution in Blasius viscous flow problems Journal of Fluid Mechanics. ,vol. 453, pp. 411- 425 ,(2002) , 10.1017/S0022112001007169
Shi-Jun Liao, An explicit, totally analytic approximate solution for Blasius’ viscous flow problems International Journal of Non-linear Mechanics. ,vol. 34, pp. 759- 778 ,(1999) , 10.1016/S0020-7462(98)00056-0