Abstract
The study is devoted to determine a solution for a non-stationary heat equation in axial symmetric cylindrical coordinates under mixed discontinuous boundary of the first and second kind conditions, with the aid of a Laplace transform and separation of variables method used to solve the considered problem which is the dual integral equations method.
Highlights
The method of dual integral equations is widely used to solve elliptic partial differential equation with many physical and technical applications[1,2,3,4], several techniques were developed in the last fifty years to solve dual equations with different coordinate systems. discuss In this study the solution of twodimensional non-stationary heat conduction problem in axially symmetrical cylindrical coordinates with discontinuous mixed boundary conditions first and second kind on the level surface of a semi-infinite solid cylindrical coordinates will be discussed
The solution of the problem is based on the application of dual integral equations method with the help of the Laplace transform and separation of variables
It is known that the solution of dual integral equations introduced to some type of singular integral equations of the first kind with unknown function, weight and free term depend on the parameter of a Laplace transform
Summary
The method of dual integral equations is widely used to solve elliptic partial differential equation with many physical and technical applications[1,2,3,4], several techniques were developed in the last fifty years to solve dual equations with different coordinate systems. discuss In this study the solution of twodimensional non-stationary heat conduction problem in axially symmetrical cylindrical coordinates with discontinuous mixed boundary conditions first and second kind on the level surface of a semi-infinite solid cylindrical coordinates will be discussed. The exact solution of such integral equation can be obtained by expressing its unknown function in the form of a functional series in powers of a Laplace transform parameter The main goal of given problem in this work is to extend the use of dual integral equations method to solve parabolic partial differential equations with mixed discontinuous boundary conditions, by using some discontinuous integrals technique This technique is applied to solve different type of dual equations related to diffraction theory, elasticity theory and other applications[3,4], when the second one of a dual integral equations is homogeneous. Mandrik reduced some dual equations to the Fredholm integral equation of the second kind[8,9]
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