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Sains Malaysiana 46(2)(2017): 335–347 http://dx.doi.org/10.17576/jsm-2017-4602-19
A
Novel Collocation Method Based on Residual Error Analysis for Solving
Integro-Differential Equations Using Hybrid Dickson and Taylor Polynomials
(Kaedah
Novel Kolokasi Berdasarkan Analisis Sisa Ralat untuk Menyelesaikan Persamaan
Integro-Pembezaan
yang Menggunakan Hibrid Dickson dan Polinomial Taylor)
ÖMÜR KIVANÇ
KÜRKÇÜ1*,
ERSIN
ASLAN2
& MEHMET SEZER3
1Department of
Mathematics, Faculty of Science, Celal Bayar University, Manisa 45140
Turkey
2Turgutlu Vocational
Training School, Celal Bayar University, Manisa, Turkey
3Department of
Mathematics, Faculty of Science, Celal Bayar University, Manisa 45140
Turkey
Received: 1 May 2015/Accepted: 18 June 2016
ABSTRACT
In this study, a novel matrix method based on collocation points
is proposed to solve some linear and nonlinear integro-differential
equations with variable coefficients under the mixed conditions.
The solutions are obtained by means of Dickson and Taylor polynomials.
The presented method transforms the equation and its conditions
into matrix equations which comply with a system of linear algebraic
equations with unknown Dickson coefficients, via collocation points
in a finite interval. While solving the matrix equation, the Dickson
coefficients and the polynomial approximation are obtained. Besides,
the residual error analysis for our method is presented and illustrative
examples are given to demonstrate the validity and applicability
of the method.
Keywords: Collocation and matrix methods; Dickson and Taylor
polynomials; integro-differential equations; nonlinear equations; pseudocode
ABSTRAK
Dalam kajian ini, kaedah matriks novel berdasarkan
titik kolokasi adalah dicadangkan untuk menyelesaikan persamaan
integro-pembezaan bagi sesetengah linear dan tak linear dengan pekali
pemboleh ubah dalam keadaan bercampur-campur. Penyelesaian yang diperoleh
dengan cara polinomial Dickson dan Taylor. Kaedah
yang dibentangkan mengubah persamaan serta keadaannya ke dalam persamaan
matriks yang bertepatan dengan sistem persamaan algebra linear dengan
pekali Dickson tidak diketahui, melalui titik kolokasi dalam selang
terhingga. Semasa menyelesaikan persamaan matriks ini, pekali Dickson dan penganggaran
polinomial diperoleh. Selain itu, analisis
sisa ralat bagi kaedah kami ini telah dikemukakan dan contoh ilustrasi
diberi untuk menunjukkan kesahihan dan penerapan kaedah.
Kata kunci: Kolokasi dan
kaedah matriks; polinomial Dickson dan Taylor; persamaan integro-pembezaan;
persamaan tak linear; tatasusunan
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*Corresponding author; email: omurkivanc@outlook.com
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