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Haar Wavelet
Collocation
Method for
Telegraph
Equations with
Different
Boundary
Conditions
Shahid Ahmed (1), Shah Jahan (2) and
K. S. Nisar
(3)
(1) Department
of Mathematics,
Central
University of
Haryana,
Mahendergarh-123029,
India
Email address:
shahid201344@cuh.ac.in
(2)
Department of
Mathematics, Central
University of
Haryana,
Mahendergarh-123029,
India
Email address:
Shahjahan@cuh.ac.in
(3) Department of
Mathematics, College
of Science and
Humanities in
Alkharj,
Prience Sattam Bin
Abdulaziz University
Alkharj 11942, Saudi
Arabia
Email address:
n.sooppy@psau.edu.sa
Doi :
https://doi.org/10.47013/17.1.1
Cited by :
Jordan J. Math &
Stat.,
17 (1) (2024),
1 - 21
PDF
Received on:
Jan. 2,
2023;
Accepted
on: May 30,
2023
Abstract. In this
article, we
study the Haar
wavelet
operational
matrix approach
for finding the
numerical
solutions of
hyperbolic
telegraph
equations under
suitable initial
and boundary
conditions. It
has been
approximated in
both space and
time using the
Haar wavelets
series with
unknown
coefficients.
The advantage of
the method is
that it reduces
the original
problems to a
set of algebraic
equations that
can be solved
using standard
methods. The
precision and
efficacy of the
numerical method
are shown via
numerical
examples. It has
been shown
experimentally
that the
approach is
straightforward,
precise, when
compared to some
of the current
numerical
methods.
Keywords: Collocation
point, Dirichlet
boundary
condition, Haar
wavelet, Neuman
boundary
conditions,
Operational
matrices,
Telegraph
equations.
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