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Single cell finite difference approximations of O ( kh 2 + h 4 ) for ∂ u /∂ x for one space dimensional nonlinear parabolic equation
Author(s) -
Mohanty R. K.,
Jain M. K.,
Kumar Dinesh
Publication year - 2000
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 - 10.1002/1098-2426(200007)16:4<408::aid-num5>3.0.co;2-j
Subject(s) - mathematics , partial differential equation , cartesian coordinate system , mathematical analysis , nonlinear system , space (punctuation) , parabolic partial differential equation , dirichlet boundary condition , finite difference method , boundary value problem , finite difference , partial derivative , polar coordinate system , differential equation , geometry , physics , linguistics , philosophy , quantum mechanics
We report a new two‐level explicit finite difference method of O ( kh 2 + h 4 ) using three spatial grid points for the numerical solution of $\frac{\partial u}{\partial x}$ for the solution of one‐space dimensional nonlinear parabolic partial differential equation subject to appropriate initial and Dirichlet boundary conditions. The method is shown to be unconditionally stable when applied to a linear equation. The proposed method is applicable to the problems both in cartesian and polar coordinates. Numerical examples are provided to demonstrate the efficiency and accuracy of the method discussed. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 408–415, 2000