TY - JOUR
T1 - Generalised Müntz Spectral Galerkin Methods for Singularly Perturbed Fractional Differential Equations
AU - Tao , Sun
AU - Liu , Rui-Qing
AU - Wang , Li-Lian
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 611
EP - 633
PY - 2018
DA - 2018/10
SN - 8
DO - http://doi.org/10.4208/eajam.050818.071018
UR - https://global-sci.org/intro/article_detail/eajam/12811.html
KW - Mapped Jacobi polynomials, generalised Müntz-Jacobi functions, singularly perturbed fractional differential equations, Petrov-Galerkin methods.
AB - <p style="text-align: justify;">A family of orthogonal generalised Müntz-Jacobi functions is introduced and
used for solving singularly perturbed fractional differential equations. Such basis functions
can provide much better approximation for boundary layers or endpoint singularities
than usual polynomial bases. The fractional integrals and derivatives of generalised
Müntz-Jacobi functions are accurately calculated. The corresponding Petrov-Galerkin
and Galerkin methods are very efficient. Numerical examples demonstrate a significant
improvement in the accuracy of the methods.</p>