A convergence analysis of the numerical solution of boundary-value problems by using two-dimensional Haar wavelets

Narongpol�Wichailukkana^a,*, Boriboon�Novaprateep^a,b, Chaiwoot�Boonyasiriwat^c

ABSTRACT: This study provides an analysis of the convergence of the Haar wavelet-based method for solving two-dimensional boundary value problems. The convergence analysis shows that the approximation method is of order 2. The analytical results are validated via two numerical examples.

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^a	Department�of�Mathematics, Faculty�of�Science, Mahidol�University, Rama�6�Road, Ratchathewi, Bangkok�10400�Thailand
^b	PERDO, Centre�of�Excellence�in�Mathematics, Commission�on�Higher�Education, Faculty�of�Science, Mahidol�University, Rama�6�Road, Ratchathewi, Bangkok�10400�Thailand
^c	Department�of�Physics, Faculty�of�Science, Mahidol�University, Rama�6�Road, Ratchathewi, Bangkok�10400�Thailand

* Corresponding author, E-mail: narongpol.wic@student.mahidol.ac.th

Received 3 Oct 2016, Accepted 3 Oct 2016

A convergence analysis of the numerical solution of boundary-value problems by using two-dimensional Haar wavelets

Narongpol�Wichailukkanaa,*, Boriboon�Novaprateepa,b, Chaiwoot�Boonyasiriwatc

Narongpol�Wichailukkana^a,*, Boriboon�Novaprateep^a,b, Chaiwoot�Boonyasiriwat^c