Communications in Numerical Methods in Engineering · 1994 · 10 citations · 4 references
Natural SciencesComputational EngineeringComputational MechanicsComputational PhysicsDifferential EquationsConvergence AnalysisDifference EquationsNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsPartial Differential EquationsFinite Difference SchemesNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsPoisson EquationPoisson's Equation
Abstract We present in this paper a nine‐point, fourth‐order difference scheme for the numerical solution of the quasilinear Poisson equation in polar co‐ordinates, with appropriate boundary conditions. A separate difference scheme of order four valid at r = 0 has also been obtained. The method is based on five evaluations of the function f. The numerical results of two problems obtained using this scheme are listed. The numerical results demonstrate the fourth‐order accuracy of the scheme.
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