(17) In the paper titled "A Compact Difference Scheme for Solving Fractional Neutral
Parabolic Differential Equation with Proportional Delay," a linearized compact finite difference scheme was constructed for solving the fractional neutral
parabolic differential equation with proportional delay.
Some oscillation results are also given for the delay
parabolic differential equation as follows:
Jones, "Determination of a coefficient in a
parabolic differential equation, I.
In this paper, we consider the following fractional neutral
parabolic differential equation with proportional delay:
Liu, "Inverse coefficient problems for nonlinear
parabolic differential equations," Acta Mathematica Sinica, vol.
Tian, "Asymptotic stability analysis of the linear [theta]-Method for linear
parabolic differential equations with delay," Journal of Difference Equations and Applications, vol.
Lin, "Determination of a parameter p(t) in some quasi-linear
parabolic differential equations," Inverse Problems, vol.
We notice that in all later published papers the theory of the finite difference method for the
parabolic differential equations with various types of nonlocal conditions was created as fully-implicit or explicit schemes theory.
Zhang, "A compact difference scheme combined with extrapolation techniques for solving a class of neutral delay
parabolic differential equations," Applied Mathematics Letters, vol.
Sun, "A Crank-Nicolson scheme for a class of delay nonlinear
parabolic differential equations," Journal on Numerical Methods and Computer Applications, vol.
Simultaneous space-time adaptive wavelet solution of nonlinear
parabolic differential equations. J.
On nonexistence of global solutions of some semilinear
parabolic differential equations. Proceedings of the Japan Academy, 49(7):503-505, 1973.