Abstract
We present an efficient modern strategy for solving some well-known classes of uncertain integral equations arising in engineering and physics fields. The solution methodology is based on generating an orthogonal basis upon the obtained kernel function in the Hilbert space W 2 1 a, b in order to formulate the analytical solutions in a rapidly convergent series form in terms of their α -cut representation. The approximation solution is expressed by n -term summation of reproducing kernel functions and it is convergent to the analytical solution. Our investigations indicate that there is excellent agreement between the numerical results and the RKHS method, which is applied to some computational experiments to demonstrate the validity, performance, and superiority of the method. The present work shows the potential of the RKHS technique in solving such uncertain integral equations.
| Original language | English |
|---|---|
| Article number | 2920463 |
| Journal | Journal of Function Spaces |
| Volume | 2016 |
| DOIs | |
| Publication status | Published - 2016 |
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ASJC Scopus subject areas
- Analysis
Cite this
Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method. / Gumah, Ghaleb; Moaddy, Khaled; Al-Smadi, Mohammed; Hashim, Ishak.
In: Journal of Function Spaces, Vol. 2016, 2920463, 2016.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method
AU - Gumah, Ghaleb
AU - Moaddy, Khaled
AU - Al-Smadi, Mohammed
AU - Hashim, Ishak
PY - 2016
Y1 - 2016
N2 - We present an efficient modern strategy for solving some well-known classes of uncertain integral equations arising in engineering and physics fields. The solution methodology is based on generating an orthogonal basis upon the obtained kernel function in the Hilbert space W 2 1 a, b in order to formulate the analytical solutions in a rapidly convergent series form in terms of their α -cut representation. The approximation solution is expressed by n -term summation of reproducing kernel functions and it is convergent to the analytical solution. Our investigations indicate that there is excellent agreement between the numerical results and the RKHS method, which is applied to some computational experiments to demonstrate the validity, performance, and superiority of the method. The present work shows the potential of the RKHS technique in solving such uncertain integral equations.
AB - We present an efficient modern strategy for solving some well-known classes of uncertain integral equations arising in engineering and physics fields. The solution methodology is based on generating an orthogonal basis upon the obtained kernel function in the Hilbert space W 2 1 a, b in order to formulate the analytical solutions in a rapidly convergent series form in terms of their α -cut representation. The approximation solution is expressed by n -term summation of reproducing kernel functions and it is convergent to the analytical solution. Our investigations indicate that there is excellent agreement between the numerical results and the RKHS method, which is applied to some computational experiments to demonstrate the validity, performance, and superiority of the method. The present work shows the potential of the RKHS technique in solving such uncertain integral equations.
UR - http://www.scopus.com/inward/record.url?scp=84979771469&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84979771469&partnerID=8YFLogxK
U2 - 10.1155/2016/2920463
DO - 10.1155/2016/2920463
M3 - Article
VL - 2016
JO - Journal of Function Spaces
JF - Journal of Function Spaces
SN - 2314-8896
M1 - 2920463
ER -