Method of independent fluxes for numerical solution of multidimensional heat equation

A new approach for the construction of unconditionally stable numerical algorithms for the solution of the multidimensional heat equation for orthogonal coordinate systems is presented. The corresponding methods (both first and second order of accuracy in time) are absolutely economical and parallelizable. This approach can be applied to multiply connected domains as well. The key element of the method is the calculation of fluxes along each spatial direction independently of one another.