Solving Initial Value Problem in Composite Materials for Heat Equation

Al-Mahdawi H. K.¹, Alhumaima Ali Subhi ¹, Hussein Alkattan^*2, Mohamed Saber ³, Marwa M. Eid ⁴, Anfal A. Sabti Al-Mahdawi¹, Jinan A. M. Al-Saddaee¹

¹ University of Diyala, Diyala ,32001, Iraq

² Department of System Programming, South Ural State University, Chelyabinsk 454080, Russia

³Electronics and Communications Engineering Department, Faculty of Engineering, Delta University for Science and Technology, Gamasa City 11152, Egypt

⁴ Faculty of Artificial Intelligence, Delta University for Science and Technology, Mansoura, Egypt

Emails: hssnkd@gmail.com; alkattan.hussein92@gmail.com; alhumaimaali@uodiyala.edu.iq; skenawy@ieee.org; mmm@ieee.org; anfal6011@gmail.com; jinanabdullahmahmood@gmail.com

Abstract

In this paper, we display the definition and arrangement of the beginning esteem issue in composite materials for warm condition. The issue includes finding the starting temperature conveyance when as it were the temperature spreading at time t=T>0 is given. Typically, a challenging issue since it has a place to a course of numerically unsteady issues that are ill-posed. To characterize this issue, we have to be present work spaces and unravel the coordinate issue to decide them. The method of division of factors is commonly utilized to fathom the coordinate issue, but it isn't reasonable for the due to the expansive blunders and disparate arrangement it produces. Ivanov V.K. proposed a strategy to get a steady inexact arrangement by supplanting the coming about arrangement with a fractional whole that depends on δ, N=N(δ). Another approach is the Picard strategy that employments a family of administrators  to map the space  into itself and get a regularized inexact arrangement. We show the comes about of computational tests and assess the viability of the Picard strategy.

Keywords: inverse problem; Picard method; ill-posed problem; composite material;