{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T12:26:44Z","timestamp":1680265604045},"reference-count":30,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2013,9]]},"abstract":"<jats:p> In this paper, two numerical methods are presented to solve an ill-posed inverse problem for Fisher's equation using noisy data. These two methods are the Haar basis and the Legendre wavelet methods combined with the Tikhonov regularization method. A sensor located at a point inside the body is used and u(x, t) at a point x = a, 0 &lt; a &lt; 1 is measured and these methods are applied to the inverse problem. We also show that an exponential rate of convergence of these methods. In fact, this work considers a comparative study between the Haar basis and the Legendre wavelet methods to solve some ill-posed inverse problems. Results show that an excellent estimation of the unknown function of the inverse problem which have been obtained within a couple of minutes CPU time at Pentium(R) Dual-Core CPU 2.20 GHz. <\/jats:p>","DOI":"10.1142\/s0219691313500343","type":"journal-article","created":{"date-parts":[[2013,7,15]],"date-time":"2013-07-15T01:43:57Z","timestamp":1373852637000},"page":"1350034","source":"Crossref","is-referenced-by-count":5,"title":["RESOLUTION OF AN INVERSE PROBLEM BY HAAR BASIS AND LEGENDRE WAVELET METHODS"],"prefix":"10.1142","volume":"11","author":[{"given":"REZA","family":"POURGHOLI","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Sciences, Damghan University, Damghan 36715-364, Iran"}]},{"given":"AMIN","family":"ESFAHANI","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Sciences, Damghan University, Damghan 36715-364, Iran"}]},{"given":"SAEDEH","family":"FOADIAN","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Sciences, Damghan University, Damghan 36715-364, Iran"}]},{"given":"SONA","family":"PAREHKAR","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Sciences, Damghan University, Damghan 36715-364, Iran"}]}],"member":"219","published-online":{"date-parts":[[2013,9,30]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2010.12.001"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-76436-3"},{"key":"rf3","volume-title":"Inverse Heat Conduction: Ill-Posed Problems","author":"Beck J. 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