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Volume 11, Issue 2
Selection of Bases in Operational Calculus and Its Applications

Li Zou, Songxin Liang, Yuan Gao & David J. Jeffrey

DOI: 10.4208/nmtma.OA-2017-0071

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 383-397.

Published online: 2018-11

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  • Abstract

In this article, we present a new method for selecting a base that corresponds to the modified left shift operator in operational calculus. The method is illustrated by Emden-Fowler equation and differential equations with variable coefficients. The method, combined with Pade approximant, is also applied to solve a differential-difference equation which was solved by the Adomian decomposition method. Since the new method does not involve integrals, it is more efficient than the one in the literature.

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@Article{NMTMA-11-383, author = {Li Zou, Songxin Liang, Yuan Gao and David J. Jeffrey}, title = {Selection of Bases in Operational Calculus and Its Applications}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {2}, pages = {383--397}, abstract = {

In this article, we present a new method for selecting a base that corresponds to the modified left shift operator in operational calculus. The method is illustrated by Emden-Fowler equation and differential equations with variable coefficients. The method, combined with Pade approximant, is also applied to solve a differential-difference equation which was solved by the Adomian decomposition method. Since the new method does not involve integrals, it is more efficient than the one in the literature.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0071}, url = {http://global-sci.org/intro/article_detail/nmtma/12435.html} }
TY - JOUR T1 - Selection of Bases in Operational Calculus and Its Applications AU - Li Zou, Songxin Liang, Yuan Gao & David J. Jeffrey JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 383 EP - 397 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.OA-2017-0071 UR - https://global-sci.org/intro/article_detail/nmtma/12435.html KW - AB -

In this article, we present a new method for selecting a base that corresponds to the modified left shift operator in operational calculus. The method is illustrated by Emden-Fowler equation and differential equations with variable coefficients. The method, combined with Pade approximant, is also applied to solve a differential-difference equation which was solved by the Adomian decomposition method. Since the new method does not involve integrals, it is more efficient than the one in the literature.

Li Zou, Songxin Liang, Yuan Gao and David J. Jeffrey. (2018). Selection of Bases in Operational Calculus and Its Applications. Numerical Mathematics: Theory, Methods and Applications. 11 (2). 383-397. doi:10.4208/nmtma.OA-2017-0071
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