Mathematical Methods in the Applied Sciences · 2014 · 10 citations · 8 references
Natural SciencesMathematicsComputational Fluid DynamicsComputational MechanicsDifferential EquationsBoundary ConditionsBoundary-value ProblemsFinite Difference MethodsNumerical Methods For Differential EquationsNumerical StabilityPartial Differential EquationsElliptic Boundary-value ProblemsElliptic Partial Differential EquationsFinite Difference DiscretizationFinite Difference SchemesNumerical Solutions Of Partial Differential EquationsParabolic Boundary-value ProblemsStability Of Finite Difference Schemes
In the present paper, we consider nonclassical problems for multidimensional elliptic equations. A finite difference method for solving these nonlocal boundary value problems is presented. Stability, almost coercive stability and coercive stability for the solutions of first and second orders of approximation are obtained. The theoretical statements for the solutions of these difference schemes are supported by numerical examples for the two‐dimensional elliptic equations. Copyright © 2014 John Wiley & Sons, Ltd.
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