A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equations
ملخص البحث
The time-fractional coupled Korteweg–de Vries (KdV) system is a generalization
of the classical coupled KdV system and obtained by replacing the first order
time derivatives by fractional derivatives of orders ν1 and ν2, (0 < ν1, ν2 ≤ 1). In this
paper, an accurate and robust numerical technique is proposed for solving the timefractional
coupled KdV equations. The shifted Legendre polynomials are introduced
as basis functions of the collocation spectral method together with the operational
matrix of fractional derivatives (described in the Caputo sense) in order to reduce
the time-fractional coupled KdV equations into a problem consisting of a system of
algebraic equations that greatly simplifies the problem. In order to test the efficiency
and validity of the proposed numerical technique, we apply it to solve two numerical
examples.
الكلمات المفتاحيه
Coupled KdV equation · Operational matrix · Gauss quadrature · Collocation spectral method · Caputo derivative