Conservative averaging as an approximate method for solution of some direct and inverse heat transfer problems

Abstract

The conservative averaging method was developed as an approximate analytical and/or numerical method for solving partial differential equation or its system with piece-wise constant (continuous) coefficients. The usage of this approximate method for separate relatively thin sub-domain or/and for subdomain with al large heat conduction coefficient leads to a reduction of domain in which the solution must be found. To apply this method for all sub-domains of layered media, a special type of spline was constructed: the integral averaged values interpolating parabolic spline. The usage of this spline allows diminishing the dimensions of initial problem per one. It is important that in all cases the original problem with discontinuous coefficients from R n+1 transforms to problem with continuous coefficients in R n . A method of conservative averaging for ill-posed inverse problems in some cases allows transforming them to wellposed inverse problems.