Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem
In this work, the triple convolution of Daubechies wavelet is used to solve the three dimensional (3D) microscale Dual Phase Lag (DPL) problem. Also, numerical solution of 3D time-dependent initial-boundary value problems of a microscopic heat equation is presented. To generate a 3D wavelet we used...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2019-07-01
|
| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | http://scma.maragheh.ac.ir/article_34964_77ed9cb99d204ba85bfaff80a1632893.pdf |
| _version_ | 1811195328280395776 |
|---|---|
| author | Zahra Kalateh Bojdi Ataollah Askari Hemmat Ali Tavakoli |
| author_facet | Zahra Kalateh Bojdi Ataollah Askari Hemmat Ali Tavakoli |
| author_sort | Zahra Kalateh Bojdi |
| collection | DOAJ |
| description | In this work, the triple convolution of Daubechies wavelet is used to solve the three dimensional (3D) microscale Dual Phase Lag (DPL) problem. Also, numerical solution of 3D time-dependent initial-boundary value problems of a microscopic heat equation is presented. To generate a 3D wavelet we used the triple convolution of a one dimensional wavelet. Using convolution we get a scaling function and a sevenfold 3D wavelet and all of our computations are based on this new set to approximate in 3D spatial. Moreover, approximation in time domain is based on finite difference method. By substitution in the 3D DPL model, the differential equation converts to a linear system of equations and related system is solved directly. We use the Lax-Richtmyer theorem to investigate the consistency, stability and convergence analysis of our method. Numerical results are presented and compared with the analytical solution to show the efficiency of the method. |
| first_indexed | 2024-04-12T00:41:37Z |
| format | Article |
| id | doaj.art-4b06472da1f44151ade2ae8d1cc20219 |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-04-12T00:41:37Z |
| publishDate | 2019-07-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-4b06472da1f44151ade2ae8d1cc202192022-12-22T03:55:00ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002019-07-01151496310.22130/scma.2018.74791.32134964Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL ProblemZahra Kalateh Bojdi0Ataollah Askari Hemmat1Ali Tavakoli2Department of Mathematics, Faculty of Science and New Technologies, Graduate University of Advanced Technology, Kerman, Iran.Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.Mathematics department, University of Mazandaran, Babolsar, Iran.In this work, the triple convolution of Daubechies wavelet is used to solve the three dimensional (3D) microscale Dual Phase Lag (DPL) problem. Also, numerical solution of 3D time-dependent initial-boundary value problems of a microscopic heat equation is presented. To generate a 3D wavelet we used the triple convolution of a one dimensional wavelet. Using convolution we get a scaling function and a sevenfold 3D wavelet and all of our computations are based on this new set to approximate in 3D spatial. Moreover, approximation in time domain is based on finite difference method. By substitution in the 3D DPL model, the differential equation converts to a linear system of equations and related system is solved directly. We use the Lax-Richtmyer theorem to investigate the consistency, stability and convergence analysis of our method. Numerical results are presented and compared with the analytical solution to show the efficiency of the method.http://scma.maragheh.ac.ir/article_34964_77ed9cb99d204ba85bfaff80a1632893.pdfMRAHeat equationwavelet methodFinite difference |
| spellingShingle | Zahra Kalateh Bojdi Ataollah Askari Hemmat Ali Tavakoli Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem Sahand Communications in Mathematical Analysis MRA Heat equation wavelet method Finite difference |
| title | Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem |
| title_full | Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem |
| title_fullStr | Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem |
| title_full_unstemmed | Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem |
| title_short | Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem |
| title_sort | application of convolution of daubechies wavelet in solving 3d microscale dpl problem |
| topic | MRA Heat equation wavelet method Finite difference |
| url | http://scma.maragheh.ac.ir/article_34964_77ed9cb99d204ba85bfaff80a1632893.pdf |
| work_keys_str_mv | AT zahrakalatehbojdi applicationofconvolutionofdaubechieswaveletinsolving3dmicroscaledplproblem AT ataollahaskarihemmat applicationofconvolutionofdaubechieswaveletinsolving3dmicroscaledplproblem AT alitavakoli applicationofconvolutionofdaubechieswaveletinsolving3dmicroscaledplproblem |