A Collocation Procedure for Treating the Time-Fractional FitzHugh–Nagumo Differential Equation Using Shifted Lucas Polynomials
Mathematics,
Journal Year:
2024,
Volume and Issue:
12(23), P. 3672 - 3672
Published: Nov. 23, 2024
This
work
employs
newly
shifted
Lucas
polynomials
to
approximate
solutions
the
time-fractional
Fitzhugh–Nagumo
differential
equation
(TFFNDE)
relevant
neuroscience.
Novel
essential
formulae
for
are
crucial
developing
our
suggested
numerical
approach.
The
analytic
and
inversion
formulas
introduced,
after
that,
new
that
express
these
polynomials’
integer
fractional
derivatives
derived
facilitate
construction
of
operational
matrices
derivatives.
Employing
with
typical
collocation
method
converts
TFFNDE
into
a
system
algebraic
equations
can
be
addressed
standard
solvers.
convergence
analysis
expansion
is
carefully
investigated.
Certain
inequalities
involving
golden
ratio
established
in
this
context.
evaluated
using
several
examples
verify
its
applicability
efficiency.
Language: Английский
Approximate Petrov–Galerkin Solution for the Time Fractional Diffusion Wave Equation
Mathematical Methods in the Applied Sciences,
Journal Year:
2025,
Volume and Issue:
unknown
Published: April 20, 2025
ABSTRACT
This
paper
discusses
the
Petrov–Galerkin
method's
application
in
solving
time
fractional
diffusion
wave
equation
(TFDWE).
The
method
is
based
on
using
two
modified
sets
of
shifted
fourth‐kind
Chebyshev
polynomials
(FKCPs)
as
basis
functions.
explicit
forms
all
spectral
matrices
were
reported.
These
are
essential
to
transforming
TFDWE
and
its
underlying
homogeneous
conditions
into
a
matrix
system.
An
appropriate
algorithm
can
be
used
solve
this
system
obtain
desired
approximate
solutions.
error
analysis
was
studied
depth.
Four
numerical
examples
provided
that
included
comparisons
with
other
existing
methods
literature.
Language: Английский