TY - JOUR
ID - 34964
TI - Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Kalateh Bojdi, Zahra
AU - Askari Hemmat, Ataollah
AU - Tavakoli, Ali
AD - Department of Mathematics, Faculty of Science and New Technologies, Graduate University of Advanced Technology, Kerman, Iran.
AD - Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman,
Kerman, Iran.
AD - Mathematics department, University of Mazandaran, Babolsar, Iran.
Y1 - 2019
PY - 2019
VL - 15
IS - 1
SP - 49
EP - 63
KW - MRA
KW - Heat equation
KW - wavelet method
KW - Finite difference
DO - 10.22130/scma.2018.74791.321
N2 - 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.
UR - https://scma.maragheh.ac.ir/article_34964.html
L1 - https://scma.maragheh.ac.ir/article_34964_77ed9cb99d204ba85bfaff80a1632893.pdf
ER -