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Sains Malaysiana 48(3)(2019): 677684 http://dx.doi.org/10.17576/jsm-2019-4803-22
Fifth Order Multistep Block Method for
Solving Volterra Integro-Differential
Equations of Second Kind (Kaedah Blok
Berbilanglangkah Peringkat Lima
bagi Penyelesaian Persamaan Pembezaan - Kamiran Volterra Jenis Kedua) ZANARIAH ABDUL
MAJID1,2* & NURUL ATIKAH
MOHAMED1 1Institute for Mathematical
Research, Universiti Putra Malaysia,
43400 UPM Serdang, Selangor Darul Ehsan,
Malaysia 2Mathematics Department,
Faculty of Science, Universiti Putra
Malaysia, 43400 UPM Serdang, Selangor
Darul Ehsan, Malaysia Diserahkan: 3 Julai 2018/Diterima: 21 November
2018 ABSTRACT In the present paper, the multistep
block method is proposed to solve the linear and non-linear Volterra integro-differential equations
(VIDEs) of the second kind using constant step size. The
proposed block method of order five consists of two point block
method presented as in the simple form of Adams Moulton type.
The numerical solutions are obtained at two new values simultaneously
at each of the integration step. In VIDEs, the unknown function appears in the form of derivative
and under the integral sign. The approximation of the integral
part is estimated using the Booles quadrature rule. The stability
region is shown, and the numerical results are presented to illustrate
the performance of the proposed method in terms of accuracy, total
function calls and execution times compared to the existing method.
Keywords: Block method; quadrature
rule; Volterra integro-differential
equation ABSTRAK Dalam makalah ini, kaedah
blok berbilanglangkah
dicadangkan bagi
menyelesaikan persamaan pembezaan-kamiran Volterra (PPKV)
linear dan tak
linear daripada jenis kedua menggunakan saiz langkah yang malar. Kaedah blok
peringkat lima yang dicadangkan
terdiri daripada
dua titik blok
yang dibentangkan dalam
bentuk yang mudah daripada jenis Adams Moulton. Penyelesaian berangka diperoleh dalam dua nilai baru
pada masa yang sama
di setiap langkah
kamiran. Dalam PPKV,
fungsi yang tidak
diketahui muncul dalam bentuk terbitan
dan tanda
kamiran. Penghampiran bahagian kamiran
dianggarkan dengan
menggunakan peraturan kuadratur Boole. Rantau kestabilan
ditunjukkan dan
keputusan berangka dibentangkan untuk menggambarkan prestasi kaedah yang dicadangkan daripada segi kejituan,
jumlah panggilan
fungsi dan masa pelaksanaan berbanding kaedah sedia ada. Kata kunci: Aturan
kuadratur; kaedah
blok; persamaan
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54(189): 155-168. *Pengarang untuk surat-menyurat; email: zana_majid99@yahoo.com
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