High accuracy difference schemes for the system of two space nonlinear parabolic differential equations with mixed derivatives and variable coefficients

• Published in: Journal of computational and applied mathematics Vol. 70; no. 1; pp. 15 - 32
• Main Authors: Mohanty, R.K., Jain, M.K.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 14.06.1996; Elsevier
• Subjects: ADI method; Difference method; Exact sciences and technology; Mathematics; Navier-Stokes' equations; Numerical analysis; Numerical analysis. Scientific computation; Parabolic equation; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Polar coordinates; Sciences and techniques of general use; Navier-Stokes' equations; Parabolic equation; Difference method; ADI method; Polar coordinates; Alternating direction method; Nonlinear equations; Boundary value problems; Partial differential equations; Polar coordinate; Numerical methods; Initial value problem; Two level method; Navier Stokes equations; Equation system; Two dimensional equation; Dirichlet problem; Finite difference method
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/0377-0427(95)00135-2

In this article, two-level compact implicit difference methods of O( k 2 + kh 2 + h 4) using 9-spatial grid points are proposed for the numerical solution of the system of two-dimensional nonlinear parabolic equations with variable coefficients subject to the Dirichlet boundary conditions, where k > 0 and h > 0 are step lengths in time and space directions, respectively. The proposed difference method for scalar equation is applied for the solution of the heat conduction equation in polar coordinates to obtain the two-level unconditionally stable ADI method of O( k 2 + h 4). The method having two variables also has been successfully applied on two-dimensional unsteady Navier-Stokes' model equations in polar coordinates. Some numerical examples are presented to demonstrate the accuracy of the implementation.