Dual Series Method for Solving a Heat Equation with Mixed Boundary Conditions

Abstract

The paper is devoted to solving a nonhomogeneous nonstationary heat equation in cylindrical coordinates with a nonaxial symmetry. This equation is subjected to nonhomogeneous, mixed, and discontinuous boundary conditions of the second and third kinds that are specified on the disk of a finite cylinder surface. In fact, the solution of the given problem is obtained by using a new type of dual series equations (DSEs) with a Bessel function of the first kind. In particular, DSEs reduce the problem to a Fredholm integral equation of the second kind which can be solved numerically by several efficient methods.