University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Application of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem49633496410.22130/scma.2018.74791.321ENZahraKalateh BojdiDepartment of Mathematics, Faculty of Science and New Technologies, Graduate University of Advanced Technology, Kerman, Iran.AtaollahAskari HemmatDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman,
Kerman, Iran.AliTavakoliMathematics department, University of Mazandaran, Babolsar, Iran.Journal Article20171104In 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.https://scma.maragheh.ac.ir/article_34964_77ed9cb99d204ba85bfaff80a1632893.pdf