Prof. Dr. Zakia HAMMOUCH
Moulay Ismail University Morocco

An efficient algorithm to solve nonlinear reaction-diffusion problems with non-integer order derivatives

In this talk present a numerical analysis of two types of nonlinear reaction-diffusion problems with periodic conditions and initial conditions, where the order of differentiation is arbitrary. Two iterative schemes are constructed using the upper and lower solutions method, which converges monotonically towards a maximum solution, or a minimum solution of the problem considered when the mesh decreases to zero, depending on whether the initial iteration is an upper solution or a lower solution. Besides, a result for comparing the different monotonic sequences is stated proved and theoretical results are supported by some numerical simulations. Keywords: Caputo derivative; Conformable derivative; Monotone iterative method; Nonlinear parabolic PDE, Upper and lower solutions.