A new method of finding strong approximation to solutions to some IBVPs

Abstract

It has been proved that every solution to a 1D initial boundary value problem (IBVP) represented by a uniformly convergent series in some domain can be approximated by a Fourier cosine series. The new series is also uniformly convergent in that domain. The strong approximation to the heat-conduction problem subject to any boundary conditions with the application of the Fourier cosine series is found. It is the Fourier cosine series approximation to the exact solution to the problem under consideration. Its coefficients form an infinite set of ordinary differential equations (ISODE). Numerical results presented for heat conduction problems show — in comparison with solutions derived by the method of seperation of variables — that relatively small number of terms of the Cosine Series approximate very well the exact solutions.