Iterative method for the numerical solution of a system of integral equations for the heat conduction initial boundary value problem

摘要

The paper deals with a numerical algorithm to reduce the overall system of integral equations describing the heat transfer process at any geometrically complex area (both two-dimensional and three-dimensional), to the iterative solution of a system of independent one-dimensional integral equations. This approach has been called 'string method' and has been used to solve a number of applications, including the problem of the detonation wave front for the calculation of heat loads in pulse detonation engines. In this approach 'the strings' are a set of limited segments parallel to the coordinate axes, into which the whole solving area is divided (similar to the way the strings are arranged in a tennis racket). Unlike other grid methods where often for finding solutions, the values of the desired function in the region located around a specific central point here in each iteration step is determined by the solution throughout the length of the one-dimensional 'string', which connects the two end points and set them values and determine the temperature distribution along all the strings in the first step of an iterative procedure.