Open Access

ARTICLE

Compact Local Stencils Employed With Integrated RBFs For Fourth-Order Differential Problems

T.-T. Hoang-Trieu¹, N. Mai-Duy¹, T. Tran-Cong¹

Structural Longevity 2011, 6(2), 93-107. https://doi.org/10.3970/sl.2011.006.093

Abstract

In this paper, new compact local stencils based on integrated radial basis functions (IRBFs) for solving fourth-order ordinary differential equations (ODEs) and partial differential equations (PDEs) are presented. The integration constants arising from the construction of IRBFs are exploited to incorporate into the local IRBF approximations values of the ODEs/PDEs at selected nodal points. The proposed stencils, which lead to sparse system matrices, are numerically validated through the solution of several analytic test problems. Numerical results indicate that their solutions converge very fast with grid refinement.

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Keywords

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