Approximate Solution of Boundary Value Problem for Heat Equation after Represented by Volterra Integral Equation of the First Kind
H.K. Al-Mahdawi 1, Mostafa Abotaleb 2, Hussein Alkattan 2, El-Sayed M El-kenawy *3
1 Electronic Computer Centre, University of Diyala, Diyala ,32001, Iraq
2 Department of System Programming, South Ural State University, 454080 Chelyabinsk, Russia
3 Department of Communications and Electronics, Delta Higher Institute of Engineering and Technology, Mansoura 35111, Egypt
Emails: hssnkd@gmail.com; abotalebmostafa@bk.ru; alkattan.hussein92@gmail.com; skenawy@ieee.org
Abstract
In this work, we study the regularization method for solving the Boundary Value Problem (BVP) for heat equation. The discretization method applied with two variables on Volterra integral equation in order to covert the problem into a linear operator equation after applied the separation of variables method to solve the partial differential equation. The regularization way used to obtain the estimate solution by using the Lavrentiev regularization method.
Keywords: Ill-posed problem; Lavrentiev regularization; Inverse problem; Heat conduction