Two-dimensional nonlinear time fractional reaction–diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media

Abstract

In the present article, an efficient operational matrix based on the famous Laguerre polynomials is applied for the numerical solution of two-dimensional non-linear time fractional order reaction–diffusion equation. An operational matrix is constructed for fractional order differentiation and this operational matrix converts our proposed model into a system of non-linear algebraic equations through collocation which can be solved by using the Newton Iteration method. Assuming the surface layers are thermodynamically variant under some specified conditions, many insights and properties are deduced e.g., nonlocal diffusion equations and mass conservation of the binary species which are relevant to many engineering and physical problems. The salient features of present manuscript are finding the convergence analysis of the proposed scheme and also the validation and the exhibitions of effectiveness of the method using the order of convergence through the error analysis between the numerical solutions applying the proposed method and the analytical results for two existing problems. The prominent feature of the present article is the graphical presentations of the effect of reaction term on the behavior of solute profile of the considered model for different particular cases.

An Accurate Numerical Scheme for Three-Dimensional Variable-Order Time-Fractional Partial Differential Equations in Two Types of Space Domains

“…Example 2. Consider the following three-dimensional non-linear variable-order time-fractional advection-reaction-diffusion equation [15]:…”

“…In order to compare the results with method [15], we listed the maximum absolute error and CPU time for γ(x, t) = 0.9 and M = 2 in Table 2. The results illustrate that the proposed method is more efficient than method [15]. Furthermore, the plots of the absolute error in the different domains are shown in Figures 1 and 2.…”

A novel fractional mathematical model of COVID-19 epidemic considering quarantine and latent time

“…The effectiveness and variation of the degree of approximation r is discussed in the literature [17] . One can easily understand that the order of convergence of the numerical techniques provided in this article [17] is increases as we increase the degree of approximation and the errors in computing the numerical solution is decreases as we increase the degree of approximation. In the present article we consider the degree approximation for each numerical computation and pictorial presentation.…”

Fibonacci polynomials for the numerical solution of variable‐order space‐time fractional Burgers‐Huxley equation

“…The results of the implementation confirm the accuracy and efficiency of the method. It is noteworthy that the method presented in this paper can be adopted for the constant-order fractional differential equations, for instance, the ones studied in Pandey et al 28,29 and Kumar et al 30…”