Original scientific paper
Direct operational matrix approach for weakly singular Volterra integro-differential equations: application in theory of anomalous diffusion
Khosrow Maleknejad
; School of Mathematics, Iran University of Science and Technology, Tehran, Iran
Raziyeh Dehbozorgi
; School of Mathematics, Iran University of Science and Technology, Tehran, Iran
Morteza Garshasbi
; School of Mathematics, Iran University of Science and Technology, Tehran, Iran
Abstract
In the current paper, we present an efficient direct scheme for weakly singular
Volterra integro-differential equations arising in the theory of anomalous diffusion. The
behavior of the system demonstrating the anomalous diffusion is significant for small times.
The method is based on operational matrices of Chebyshev and Legendre polynomials with
some techniques to reduce the total errors of the already existing schemes. The proposed
scheme converts these equations into a linear system of algebraic equations. The main
advantages of the method are high accuracy, simplicity of performing, and low storage
requirement. The main focus of this study is to obtain an analytical explicit expression
to estimate the error. Numerical results confirm the superiority and applicability of our
scheme in comparison with other methods in the literature.
Keywords
Direct numerical scheme; weakly singular; Volterra integro-differential equations; operational matrix; anomalous diffusion; error estimation
Hrčak ID:
215150
URI
Publication date:
19.4.2019.
Visits: 965 *