An efficient meshless computational technique to simulate nonlinear anomalous reaction–diffusion process in two-dimensional space

Nonlinear Dynamics - In this paper, a numerical simulation of an anomalous reaction–diffusion process in two-dimensional space with a nonlinear source term is presented. An efficient and...     

The method of approximate particular solutions to simulate an anomalous mobile-immobile transport process

In the current work, a generalized mathematical model based on the Coimbra time fractional derivative of variable order, which describes an anomalous mobile-immobile transport process in complex systems is investigated numerically. A robust numerical technique based on the meshfree strong form method combined with an efficient time-stepping scheme is performed to compute the approximate solution of the problem with high accuracy. For this purpose, firstly, an effective implicit time discretization approach is used for discretizing the variable-order time fractional problem in the time direction. Then a global meshless technique based on the method of approximate particular solutions is performed to fully discretize the model in the spatial domain. The validity and performance of the procedure to numerically simulate the proposed generalized solute transport model on regular and irregular domains are demonstrated through some numerical examples.     

Convergence of the variational iteration method for the telegraph equation with integral conditions

In this article, we first transform the telegraph equation into a system of partial differential equations. Then, we apply the variational iteration method to compute an approximate solution for the telegraph equation. Convergence of the proposed method is also discussed. Finally, some numerical examples are given to show the effectiveness of the proposed method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1442–1455, 2011     

MHD Falkner-Skan flow of Maxwell fluid by rational Chebyshev collocation method

The magnetohydrodynamics （MHD） Falkner-Skan flow of the Maxwell fluid is studied. Suitable transform reduces the partial differential equation into a nonlinear three order boundary value problem over a semi-infinite interval. An efficient approach based on the rational Chebyshev collocation method is performed to find the solution to the proposed boundary value problem. The rational Chebyshev collocation method is equipped with the orthogonal rational Chebyshev function which solves the problem on the semi-infinite domain without truncating it to a finite domain. The obtained results are presented through the illustrative graphs and tables which demonstrate the affectivity, stability, and convergence of the rational Chebyshev collocation method. To check the accuracy of the obtained results, a numerical method is applied for solving the problem. The variations of various embedded parameters into the problem are examined.