On the joint application of the collocation boundary element method and the Fourier method for solving problems of heat conduction in finite cylinders with smooth directrices

The solution of heat conduction problems in a straight cylinder with zero boundary conditions on the bases and zero initial condition is investigated using the combined use of the collocation method of boundary elements and the Fourier method. Due to the moderate mesh refinement, which compensates for the drop in accuracy for large eigenvalues of the differential operator $\partial^{2}_{уу}$ with the corresponding zero boundary conditions, approximate solutions are obtained that stably converge to exact ones with a cubic velocity uniformly with respect to the generator length and uniformly with respect to the sets of boundary functions bounded in the norm of functions with low smoothness in the variable $y$. The theoretical conclusions are confirmed by the results of the numerical solution of the problem in a circular cylinder.