In this paper, the comparison of finite difference and Fourier spectral numerical methods for an inverse problem of simultaneously determining an unknown coefficient in a parabolic equation with the usual initial and boundary conditions is proposed. We represent the detailed description of the methods and their algorithms. The research work conducted in this paper shows that the Fourier spectral method is highly accurate.
Fourier spectral method, parabolic equation, inverse problem, numerical algorithm, overdetermination condition
DURDIEV, DURDIMUROD and DURDIEV, DILSHOD
"The Fourier spectral method for determining a heat capacity coefficient in a parabolic equation,"
Turkish Journal of Mathematics: Vol. 46:
8, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss8/11