مشخصات پژوهش

صفحه نخست /An accurate kernel ...
عنوان An accurate kernel functions-based method for coupled advection-diffusion-reaction models under Neumann, periodic, and no flux conditions
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها Advection-diffusion-reaction system; positive definite kernel; error analysis; Brusselator system; Schnakenberg system
چکیده This paper presents a numerical procedure for solving a class of nonlinear two and three-dimensional coupled advection-diffusion-reaction systems. First, we discrete the spatial direction using a kernel-based pseudo-spectral method. The methodology relies on positive definite kernels designed to precisely satisfy the specific boundary conditions of the problems, such as Neumann, periodic, and no flux conditions. Then, the fourth-order version of the Runge-Kutta method is used in the time direction to ensure high-order accuracy. Using this temporal discretization, we obtain an explicit scheme that does not need to solve any nonlinear systems of equations. Also, we have provided a robust error analysis for the proposed method. We performed several numerical simulations to evaluate the effectiveness and validity of the presented method. Specifically, we considered some examples of two and three-dimensional Brusselator and Schnakenberg systems and reported the results. The numerical results align completely with the analytical results.
پژوهشگران بابک آذرنوید (نفر اول)، مجتبی فردی (نفر دوم)