تحت إشراف قسم الرياضيات والإحصاء أقيم يوم الثلاثاء 17/8/1442هـ سيمنار بعنوان:
A Two-Level Factored Crank-Nicolson Method for Two-Dimensional Nonstationary Advection-Diffusion Equation With Time Dependent Dispersion Coefficients and Source Terms
قدمه د. ايريك نقونديب وذلك في تمام الساعة 8:30 مساءً عبر برنامج الزووم
ملخص البحث:
Abstract
This paper deals with a two-level factored Crank-Nicolson method in an approximate solution of two-dimensional evolutionary advection-diffusion equation with time dependent dispersion coefficients and sink/source terms subjects to appropriate initial and boundary conditions. The procedure consists to reducing problems in many space variables into a sequence of one-dimensional subproblems and then find the solution of tridiagonal linear systems of equations. This considerably reduces the computational cost of the algorithm. Furthermore, the proposed approach is fast and efficient: unconditionally stable, temporal second order accurate and fourth order convergent in space and it improves a large class of numerical schemes widely studied in the literature for the considered problem. The stability of the new method is deeply analyzed using the L^{∞}(t_{0},T_{f} ;L^{2} )-norm whereas the convergence rate of the scheme is numerically obtained in the L 2 -norm. A broad range of numerical experiments are presented and critically discussed.
