A New Method of Finding Approximate Solutions of the Heat Conduction Equation
The paper presents a new method of determination of approximate solution of onedimensional boundary value problem for the heat conduction equation with homogeneous mixed boundary conditions. From the numerical analysis of the problem considered for certain time instants and each particle of the layer, and for chosen particles of the layer in the whole time period, it is evident that the new solution approximates well the classical solution of the same problem achieved by the method of seperation of variables. Numerical analysis of the boundary conditions following from the new approach has shown that they become homogeneous for large values of time.
A.N. TICHONOV and A.A. SAMARSKI, Equations of mathematical physics [in Polish], PWN, Warszawa 1963.