[PDF] Top 20 Compact local integrated-RBF approximations for second-order elliptic differential problems

... conventional differential approach, namely (i) the implementation of multiple boundary conditions [18,19,20]; (ii) the imposition of the governing equation on the boundary [21] and (iii) the imposition of ... See full document

... flow problems in ...high-order compact integrated radial basis function (CIRBF) approximations for the spatial discretisation and utilises the second-order ... See full document

... curved boundaries. The strength of RBF methods lies in their ability to deal with scattered data. In the present work, this strength is exploited in the con- text of Cartesian grid discretisations. It is noted ... See full document

... used, RBF-based methods such as those using MQs are known to suffer from the so-called uncer- tainty ...condition. RBF-based methods can be classified into two categories: global and ...every RBF on ... See full document

... partial differential equations ...for problems defined on irregular ...However, RBF matrices are dense and generally ...problem, local RBF methods have been developed, resulting in ... See full document

... a compact local IRBF scheme, for the discretisation of the u b − p formulation in two ...IRBF approximations using values of the pressure at interior nodes along a grid line and first-order ... See full document

... Cartesian-grid techniques, difficulties lie in the handling of irregular boundary geometries. Since the irregular boundary does not generally pass through grid nodes (regular points), one expects to have a change in grid ... See full document

... Consider a 9-node stencil identified by the central node ( j i , ) . Assume that the stencil is locally numbered from left to right and from bottom to top (Figure 1) ( ( j i , ) ≡ node 5). Hereafter, for brevity, we will ... See full document

... mechanics problems such as the motion of a fluid and the deformation of a solid ...proposed integrated RBF (IRBF) meth- ods, in which highest-order derivative(s) in the ODE/PDE are ... See full document

... on compact integrated radial basis function (RBF) stencils and second-order Adams-Bashforth/Crank-Nicolson algorithms for solving time-dependent ...employ compact ... See full document

... The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and ... See full document

... Zienkiewicz and Zhu [14] [15] introduced the patch recovery technique which provides some superconvergence for the gradient of the finite element solution by using a discrete least-squares fitting on a local patch ... See full document

... As we know, the fixed point theorem of cone expression and compression is extensively used to study the existence of multiple solutions of boundary value problems for second- order differential ... See full document

... and second-order impulsive ordinary differential equations with boundary conditions 5–19, which are important for complementing the theory of impulsive ...value problems of first-order and ... See full document

... RBFNs are a high-order interpolation scheme (e.g. [1]). Unlike schemes based on Chebyshev polynomials and Fourier series, RBFNs do not require an underlying structured discretisation. Some RBFs such as Gaussian ... See full document

... drawbacks, local and compact local IRBF schemes have been de- veloped ...Such local schemes result in sparse system matrices and a solution to an algebraic set of equations is thus more ... See full document

... Suppose that Φ(x, a,b) takes its maximum value at P on ∂Ω. Then, by Hopf ’s second maximum principle [4, 8], we must have Φ ≡ cte in Ω or ∂Φ/∂n > 0 at P. We now com- pute the outward normal derivative ∂ Φ /∂n ... See full document

... some second-order ordinary differential systems has been extensively investigated because of its background in applied science (see [–] and the references cited ... See full document

... quasi-linear elliptic equations is ...singular problems and problems in polar coordinates. Also, new fourth-order methods for obtaining the first-order normal derivatives of the solution ... See full document

... of problems, in pure ...ational problems in which the integrand of the objective functional contains a term of a square root of the quadratic form, while in [5], Husain and Jabeen studied op- timality ... See full document