Numerical Methods for Partial Differential Equations · 1995 · 22 citations · 3 references
ComputingComputational EngineeringComputational Fluid DynamicsComputational MechanicsDifferential EquationsConvergence AnalysisFinite Difference MethodsIterative SolversNumerical AlgorithmsNumerical Methods For Differential EquationsConvergenceDifferential Equation SolversFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsTruncationTruncation ErrorTruncation Error Analysis
Abstract A finite difference scheme for the two‐dimensional, second‐order, nonlinear elliptic equation is developed. The difference scheme is derived using the local solution of the differential equation. A 13‐point stencil on a uniform mesh of size h is used to derive the finite difference scheme, which has a truncation error of order h 4 . Well‐known iterative methods can be employed to solve the resulting system of equations. Numerical results are presented to demonstrate the fourth‐order convergence of the scheme. © 1995 John Wiley & Sons, Inc.
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