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A fourth order difference method for the one-dimensional general quasilinear parabolic partial differential equation. (English) Zbl 0715.65067

The fourth order compact difference scheme for the equation \(u_{xx}=f(u,u_ t,u_ x,x,t)\) is constructed, the order of truncation error being \(O(k^ 2+kh^ 2+h^ 4)\) where k and h are the mesh sizes in t and x directions, respectively. The scheme is shown to be unconditionally stable and to give oscillation-free solutions independently on cell Reynolds number for the convection-diffusion equation with constant coefficients. Numerical examples are presented.
Reviewer: A.I.Tolstykh

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
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
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