Fourth‐order finite difference method for 2D parabolic partial differential equations with nonlinear first‐derivative terms
Copyright policy )Fourth‐order finite difference method for 2D parabolic partial differential equations with nonlinear first‐derivative terms
AbstractWe attempt to obtain a two‐level implicit finite difference scheme using nine spatial grid points of O(k2 + kh2 + h4) for solving the 2D nonlinear parabolic partial differential equation v1uxx + v2uyy = f(x, y, t, u, ux, uy, u1) where v1 and v2 are positive constants, with Dirichlet boundary conditions. The method, when applied to a linear diffusion‐convection problem, is shown to be unconditionally stable. Computational efficiency and the results of numerical experiments are discussed.
two-dimensional nonlinear parabolic differential equation, numerical examples, two-level implicit finite-difference scheme, diffusion- convection equation, high efficiency, Burger's equation, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Functional-differential equations (including equations with delayed, advanced or state-dependent argument), Nonlinear parabolic equations, unconditional stability, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, order of accuracy
two-dimensional nonlinear parabolic differential equation, numerical examples, two-level implicit finite-difference scheme, diffusion- convection equation, high efficiency, Burger's equation, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Functional-differential equations (including equations with delayed, advanced or state-dependent argument), Nonlinear parabolic equations, unconditional stability, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, order of accuracy
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