Recursive Solution for Nonlinear Integral/ Differential Equations Using PL Transform
Summary :
A new algebraic solution is developed for nonlinear integral/ differential equations including power-law or product-type nonlinearities. The new method performs the computation via PL transform using multiplication operator with the aid of integral operator through iterative calculations. This method is capable of solving integral or integro-differential equations without converting the equation into a equivalent differential equation. The method is also capable of solving higher-order differential equations without converting the equation into a set of simultaneous first order differential equations. Examples show that a good accuracy was obtained using a limited length PL transform through a small number of iterations.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E74-A No.4 pp.722-730
- Publication Date
- 1991/04/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Nonlinear Problems
Authors
Keyword
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Kazuo NOHARA, "Recursive Solution for Nonlinear Integral/ Differential Equations Using PL Transform" in IEICE TRANSACTIONS on Fundamentals,
vol. E74-A, no. 4, pp. 722-730, April 1991, doi: .
Abstract: A new algebraic solution is developed for nonlinear integral/ differential equations including power-law or product-type nonlinearities. The new method performs the computation via PL transform using multiplication operator with the aid of integral operator through iterative calculations. This method is capable of solving integral or integro-differential equations without converting the equation into a equivalent differential equation. The method is also capable of solving higher-order differential equations without converting the equation into a set of simultaneous first order differential equations. Examples show that a good accuracy was obtained using a limited length PL transform through a small number of iterations.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e74-a_4_722/_p
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@ARTICLE{e74-a_4_722,
author={Kazuo NOHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Recursive Solution for Nonlinear Integral/ Differential Equations Using PL Transform},
year={1991},
volume={E74-A},
number={4},
pages={722-730},
abstract={A new algebraic solution is developed for nonlinear integral/ differential equations including power-law or product-type nonlinearities. The new method performs the computation via PL transform using multiplication operator with the aid of integral operator through iterative calculations. This method is capable of solving integral or integro-differential equations without converting the equation into a equivalent differential equation. The method is also capable of solving higher-order differential equations without converting the equation into a set of simultaneous first order differential equations. Examples show that a good accuracy was obtained using a limited length PL transform through a small number of iterations.},
keywords={},
doi={},
ISSN={},
month={April},}
Copy
TY - JOUR
TI - Recursive Solution for Nonlinear Integral/ Differential Equations Using PL Transform
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 722
EP - 730
AU - Kazuo NOHARA
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E74-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 1991
AB - A new algebraic solution is developed for nonlinear integral/ differential equations including power-law or product-type nonlinearities. The new method performs the computation via PL transform using multiplication operator with the aid of integral operator through iterative calculations. This method is capable of solving integral or integro-differential equations without converting the equation into a equivalent differential equation. The method is also capable of solving higher-order differential equations without converting the equation into a set of simultaneous first order differential equations. Examples show that a good accuracy was obtained using a limited length PL transform through a small number of iterations.
ER -
English
