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An O ( K 2 + h 4 ) finite difference method for one‐space Burger's equation in polar coordinates
Author(s) -
Mohanty R. K.
Publication year - 1996
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199609)12:5<579::aid-num3>3.0.co;2-h
Subject(s) - mathematics , convergence (economics) , polar coordinate system , mathematical analysis , boundary value problem , space (punctuation) , grid , class (philosophy) , initial value problem , polar , geometry , computer science , physics , artificial intelligence , economics , economic growth , operating system , astronomy
A two‐level implicit difference method of O ( k 2 + h 4 ) for a class of singular initial boundary value problem, $\nu(u_{rr} + \alpha\over{r} u_r - {\beta_u}\over{r^2}) = u_t + \gamma u u_r + f(r,t),\,\, 0 < r < 1, t >0; u(r,0) = u_0(r), u(0,t) = g_0(t), u(1,t) = g_1(t)$ where α, β, γ, and ν are constants, is discussed using three spatial grid points. The method is shown to be unconditionally stable when applied to linearized equations. The fourth‐order convergence for a fixed mesh ratio parameter is illustrated with the help of two examples. © 1996 John Wiley & Sons, Inc.