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Advisor(s)
Abstract(s)
This paper derives a new operational matrix of the variable-order (VO) time fractional
partial derivative involved in anomalous diffusion for shifted Chebyshev polynomials. We
then develop an accurate numerical algorithm to solve the 1þ1 and 2þ1 VO and
constant-order fractional diffusion equation with Dirichlet conditions. The contraction of
the present method is based on shifted Chebyshev collocation procedure in combination
with the derived shifted Chebyshev operational matrix. The main advantage of the proposed
method is to investigate a global approximation for spatial and temporal discretizations,
and it reduces such problems to those of solving a system of algebraic equations,
which greatly simplifies the solution process. In addition, we analyze the convergence of
the present method graphically. Finally, comparisons between the algorithm derived in
this paper and the existing algorithms are given, which show that our numerical schemes
exhibit better performances than the existing ones.
Description
Keywords
Operational matrix Collocation method Variable-order anomalous diffusion Chebyshev polynomials
Citation
Publisher
American Society of Mechanical Engineers