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A Stabilized Rbf Collocation Scheme For Neumann Type Boundary Value Problems, Nicolas Ali Libre, Arezoo Emdadi, Edward J. Kansa, Mohammad Rahimian, Mohammad Shekarchi

Civil, Architectural and Environmental Engineering Faculty Research & Creative Works

The numerical solution of partial differential equations (PDEs) with Neumann boundary conditions (BCs) resulted from strong form collocation scheme are typically much poorer in accuracy compared to those with pure Dirichlet BCs. In this paper, we show numerically that the reason of the reduced accuracy is that Neumann BC requires the approximation of the spatial derivatives at Neumann boundaries which are significantly less accurate than approximation of main function. Therefore, we utilize boundary treatment schemes that based upon increasing the accuracy of spatial derivatives at boundaries. Increased accuracy of the spatial derivative approximation can be achieved by h-refmement reducing the …