A two-level factored Crank-Nicolson method for two-dimensional nonstationary advection-diffusion equation with time dependent dispersion coefficients and source terms. (English) Zbl 1488.65270
Summary: 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 \(L^\infty(t_0,T_f;L^2)\)-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.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
Keywords:
two-dimensional advection-diffusion equation; time dependent dispersion coefficients; Crank-Nicolson approach; two-level factored Crank-Nicolson method; stability and convergence rateReferences:
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