Monotone iterative ADI method for solving coupled systems of nonlinear parabolic equations

Boglaev, Igor

doi:10.1016/j.apnum.2016.03.009

Cited by 2 publications

(1 citation statement)

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“…If the differential operators L and B are nonlinear, it is a nonlinear system of equations, and the approximate value of nodes should be solved by the iterative method [18][19][20][21]. Monotone iterative ADI (alternating direction implicit) was used for solving coupled systems of nonlinear parabolic equations, and Boglaev [19] stopped the algorithm and the number of iterations by verifying the convergence order. e inexact Hermitian/Skew-Hermitian Splitting (IHSS) was presented for solving system of nonlinear equations [20].…”

Section: Collocation Methodmentioning

confidence: 99%

A Finite Point Method for Solving the Time Fractional Richards’ Equation

Qin

Yang

2019

Mathematical Problems in Engineering

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In this paper, we propose a numerical method for solving the time fractional Richards’ equation. We first approximate the time fractional derivative of the mentioned equations by a scheme of order O(τ2−α), 0 < a<1; then, we use the finite point method to approximate the spatial derivatives. Before the discrete spatial derivatives, we introduced the basic principles of the finite point method. We solve the one- and two-dimensional versions of these equations using the proposed method. Moreover, the stability properties of the discretized scheme related to time are theoretically analyzed. Numerical results showed the efficiency of the method presented in this paper.

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