Eman Abuteen | Al-Balqa Applied University (original) (raw)
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In this article, the reproducing kernel Hilbert space 4 2 W [0, 1] is employed for solving a clas... more In this article, the reproducing kernel Hilbert space 4 2 W [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast accurately and efficiently series solutions with easily computable coefficients throughout evolution the algorithm under constraint periodic conditions within required grid points. The analytic solution is formulated in a finite series form whilst the truncated series solution is given to converge uniformly to analytic solution. The reproducing kernel procedure is based upon generating orthonormal basis system over a compact dense interval in sobolev space to construct a suitable analytical-numerical solution. Furthermore, experiments results of some numerical examples are presented to illustrate the good performance of the presented algorithm. The results indicate that the reproducing kernel procedure is powerful tool for solving other problems of ordinary and partial differential equations arising in physics, computer and engineering fields.
Soft Computing, 2016
The user has requested enhancement of the downloaded file. All in-text references underlined in b... more The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately.
Computers & Mathematics with Applications, 2013
In this article, the reproducing kernel Hilbert space 4 2 W [0, 1] is employed for solving a clas... more In this article, the reproducing kernel Hilbert space 4 2 W [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast accurately and efficiently series solutions with easily computable coefficients throughout evolution the algorithm under constraint periodic conditions within required grid points. The analytic solution is formulated in a finite series form whilst the truncated series solution is given to converge uniformly to analytic solution. The reproducing kernel procedure is based upon generating orthonormal basis system over a compact dense interval in sobolev space to construct a suitable analytical-numerical solution. Furthermore, experiments results of some numerical examples are presented to illustrate the good performance of the presented algorithm. The results indicate that the reproducing kernel procedure is powerful tool for solving other problems of ordinary and partial differential equations arising in physics, computer and engineering fields.
The main goal of this paper is to present a new approximate series solution of the one-dimensiona... more The main goal of this paper is to present a new approximate series solution of the one-dimensional, nonlinear Klein-Gordon equations with time-fractional derivative in Caputo form using a recently semianalytical technique, called fractional reduced differential transform method (FRDTM). This technique provides the solutions very accurately and efficiently in the form of convergent series with easily computable components. The behavior of the approximate series solution for different values of fractional-order is shown graphically. A comparative study is presented between FRDTM and the Implicit Runge-Kutta method, in the case of integer-order derivative, to demonstrate the validity and applicability of the proposed technique. The results reveal that the FRDTM is a very simple, straightforward and powerful mathematical tool for a wide range of real-world phenomena arising in engineering, biology and physical sciences that modelled in terms of fractional differential equations.
In this article, the reproducing kernel Hilbert space 4 2 W [0, 1] is employed for solving a clas... more In this article, the reproducing kernel Hilbert space 4 2 W [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast accurately and efficiently series solutions with easily computable coefficients throughout evolution the algorithm under constraint periodic conditions within required grid points. The analytic solution is formulated in a finite series form whilst the truncated series solution is given to converge uniformly to analytic solution. The reproducing kernel procedure is based upon generating orthonormal basis system over a compact dense interval in sobolev space to construct a suitable analytical-numerical solution. Furthermore, experiments results of some numerical examples are presented to illustrate the good performance of the presented algorithm. The results indicate that the reproducing kernel procedure is powerful tool for solving other problems of ordinary and partial differential equations arising in physics, computer and engineering fields.
Soft Computing, 2016
The user has requested enhancement of the downloaded file. All in-text references underlined in b... more The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately.
Computers & Mathematics with Applications, 2013
In this article, the reproducing kernel Hilbert space 4 2 W [0, 1] is employed for solving a clas... more In this article, the reproducing kernel Hilbert space 4 2 W [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast accurately and efficiently series solutions with easily computable coefficients throughout evolution the algorithm under constraint periodic conditions within required grid points. The analytic solution is formulated in a finite series form whilst the truncated series solution is given to converge uniformly to analytic solution. The reproducing kernel procedure is based upon generating orthonormal basis system over a compact dense interval in sobolev space to construct a suitable analytical-numerical solution. Furthermore, experiments results of some numerical examples are presented to illustrate the good performance of the presented algorithm. The results indicate that the reproducing kernel procedure is powerful tool for solving other problems of ordinary and partial differential equations arising in physics, computer and engineering fields.
The main goal of this paper is to present a new approximate series solution of the one-dimensiona... more The main goal of this paper is to present a new approximate series solution of the one-dimensional, nonlinear Klein-Gordon equations with time-fractional derivative in Caputo form using a recently semianalytical technique, called fractional reduced differential transform method (FRDTM). This technique provides the solutions very accurately and efficiently in the form of convergent series with easily computable components. The behavior of the approximate series solution for different values of fractional-order is shown graphically. A comparative study is presented between FRDTM and the Implicit Runge-Kutta method, in the case of integer-order derivative, to demonstrate the validity and applicability of the proposed technique. The results reveal that the FRDTM is a very simple, straightforward and powerful mathematical tool for a wide range of real-world phenomena arising in engineering, biology and physical sciences that modelled in terms of fractional differential equations.