Calculation of operators, which solve problems of heat conduction in straight cylinders using semigroup symmetry

The paper discuses an efficient method for calculating network operators, which solve initial boundary value problems for the homogeneous heat conduction equation with constant coefficients in cylindrical domain with zero initial conditions and boundary conditions on the grounds and inhomogeneous boundary conditions on the lateral surface of the cylinder. The savings have been achieved through calculation of operators in the algebra of polynomials formed by power of spatial-temporal semigroup operator as well as the separation of calculations by spatial variables along element and base of cylinder. Along all the variables quadratic approximation is used. The convergence and stability of method are proved, approximation orders are obtained relatively digitalization of different variables.

boundary element method, method of separation of variables, method of operators, heat conduction