The representation of spatial discrete data is crucial for the analysis meteorology, agriculture, geological exploration and other fields. Among various methods scattered interpolation, multiquadric (MQ) method most favorable in field surface construction. However, classical MQ has accuracy concern on boundary time consuming large set. This study proposes an algorithm by integrating with trend ...

This paper presents a study for solving unsaturated flow in heterogeneous porous media using the meshless method with radial basis function (RBF). For modeling nonlinear hydrological process zone, an exponential model is introduced Richards equation such that we may obtain linearized equation. We adopt multiquadric as RBF simulating problems layered soils, flux and head must satisfy continuity ...

We consider the version of multiquadric interpolation where the interpolation conditions are the equations s(xi ) = fi , i = 1, 2, . . . , n, and where the interpolant has the form s(x) = ∑n j=1 λ j (‖x − x j‖ + c2)1/2 + α, x ∈ Rd , subject to the constraint ∑nj=1 λ j = 0. The points xi ∈ Rd , the right-hand sides fi , i = 1, 2, . . . , n, and the constant c are data. The equations and the cons...

the present study is an attempt to investigate some features of radial basis functions (rbfs) approximation methods related to variational problems. thereby authors applied some properties of rbfs to develop a direct method which reduces constrained variational problem to a static optimization problem. to assess the applicability and effectiveness of the method, some examples are examined. dyna...

The inverse multiquadric radial basis function (RBF), which is one of the most important functions in theory RBFs, employed on an adaptive mesh points for pricing a fractional Black–Scholes partial differential equation (PDE) based modified RL derivative. To solve this problem, discretization along space carried out non-uniform grid order to focus hot area, at initial condition model, i.e., pay...

In this study, we are mainly interested in error estimates of interpolation, using smooth radial basis functions such as multiquadrics. The current theories of radial basis function interpolation provide optimal error bounds when the basis function φ is smooth and the approximand f is in a certain reproducing kernel Hilbert space Fφ. However, since the space Fφ is very small when the function φ...