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Sains Malaysiana 48(12)(2019):
2807–2815 http://dx.doi.org/10.17576/jsm-2019-4812-22
Study on Numerical Solution of a
Variable Order Fractional Differential Equation based on Symmetric
Algorithm (Kajian
Penyelesaian Berangka Peringkat Berubah Persamaan Pembezaan Pecahan
berdasarkan Algoritma Simetri) Jingrui Liu & Dongyang Pan* The
School of Mathematics and Computer Science, Xinyang Vocational and
Technical College, Xinyang, 464000, China Received:
21 February 2019/ Accepted: 23 December 2019 ABSTRAK As the class of fractional differential
equations with changing order has attracted more attention and attention
in the fields of research and engineering, it is important to study
its numerical solutions. Numerical solution algorithm for a class
of fractional differential equations with transformed arrays based
on the proposed symmetry algorithm. The symmetry classification
is used for the class of values of the boundary problem of the fractional
differential equation with the order of change. A fully symmetric
classification of the boundary value problem for a class of fractional
differential equations with variable sequences is determined by
using a fully symmetric differential sequence sorting algorithm.
The problem of the boundary value of the fractional differential
equation with the transformed order is reduced to the initial value
of the ordinary differential equation. The Legendre polynomial method
is used to solve the numerical solution of the starting value of
the differential equation. The common differential equation is transformed
into a matrix series product by a different operator matrix. The
matrix products are converted to algebraic equations by discrete
variables. By solving the equations, the numerical solution of the
starting value of the common differential equation is obtained. Keywords: Boundary value problem;
differential equation; numerical solution; operator matrix; symmetric
algorithm; variable fractional order ABSTRAK Oleh kerana kelas persamaan pembezaan
pecahan dengan susunan berubah telah menarik banyak perhatian dan
perhatian dalam bidang penyelidikan dan kejuruteraan, ia amat penting
untuk mengkaji penyelesaian berangkanya. Algoritma penyelesaian
berangka untuk kelas persamaan pembezaan pecahan dengan transformasi
tatasusunan berdasarkan algoritma simetri yang dicadangkan. Pengelasan
simetri digunakan untuk nilai kelas masalah sempadan persamaan pembezaan
pecahan dengan susunan berubah. Pengelasan simetrik sepenuhnya masalah
nilai sempadan untuk kelas persamaan pembezaan pecahan dengan jujukan
pemboleh ubah ditentukan dengan menggunakan algoritma pengisihan
jujukan pembezaan simetrik sepenuhnya. Masalah nilai sempadan persamaan
pembezaan pecahan dengan peringkat berubah dikurangkan kepada masalah
nilai awal persamaan pembezaan biasa. Kaedah polinomial Legendre
digunakan untuk menyelesaikan penyelesaian berangka masalah nilai
permulaan persamaan pembezaan. Persamaan pembezaan biasa diubah
menjadi produk siri matriks oleh pengendali matriks lain. Produk
matriks ditukar kepada persamaan algebra oleh variat diskret. Dengan
menyelesaikan persamaan, penyelesaian berangka nilai permulaan persamaan
pembezaan biasa diperoleh. Kata
kunci: Algoritma simetri; masalah nilai sempadan; matriks pengendali;
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