scholarly journals Numerical Solutions of a Boundary Value Problem on the Sphere Using Radial Basis Functions

2018 ◽  
pp. 815-836
Author(s):  
Quoc T. Le Gia
Keyword(s):  
Boundary Value Problem ◽  
Radial Basis Functions ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Basis Functions ◽  
Radial Basis

COMPARATIVE STUDY OF THE MULTIQUADRIC AND THIN-PLATE SPLINE RADIAL BASIS FUNCTIONS FOR THE TRANSIENT-CONVECTIVE DIFFUSION PROBLEMS

2006 ◽  
Vol 17 (08) ◽  
pp. 1151-1169 ◽  
Author(s):  
A. DURMUS ◽  
I. BOZTOSUN ◽  
F. YASUK
Keyword(s):  
Radial Basis Functions ◽  
Thin Plate ◽  
Numerical Solutions ◽  
Convective Diffusion ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Thin Plate Spline ◽  
Collocation Methods ◽  
Radial Basis ◽  
Diffusion Problems

The numerical solutions of the unsteady transient-convective diffusion problems are investigated by using multiquadric (MQ) and thin-plate spline (TPS) radial basis functions (RBFs) based on mesh-free collocation methods with global basis functions. The results of radial basis functions are compared with the mesh-dependent boundary element and finite difference methods as well as the analytical solution for high Péclet numbers. It is reported that for low Péclet numbers, MQ-RBF provides excellent agreement, while for high Péclet numbers, TPS-RBF is better than MQ-RBF.

The meshless method of radial basis functions for the numerical solution of time fractional telegraph equation

2014 ◽  
Vol 24 (8) ◽  
pp. 1636-1659 ◽  
Author(s):  
Akbar Mohebbi ◽  
Mostafa Abbaszadeh ◽  
Mehdi Dehghan
Keyword(s):  
Radial Basis Functions ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Telegraph Equation ◽  
Basis Functions ◽  
Content Type ◽  
Fractional Telegraph Equation ◽  
Radial Basis ◽  
Collocation Approach ◽  
Derivatives Of

Purpose – The purpose of this paper is to show that the meshless method based on radial basis functions (RBFs) collocation method is powerful, suitable and simple for solving one and two dimensional time fractional telegraph equation. Design/methodology/approach – In this method the authors first approximate the time fractional derivatives of mentioned equation by two schemes of orders O(τ3−α) and O(τ2−α), 1/2<α<1, then the authors will use the Kansa approach to approximate the spatial derivatives. Findings – The results of numerical experiments are compared with analytical solution, revealing that the obtained numerical solutions have acceptance accuracy. Originality/value – The results show that the meshless method based on the RBFs and collocation approach is also suitable for the treatment of the time fractional telegraph equation.

A New Method for Solving Steady Flow of a Third-Grade Fluid in a Porous Half Space Based on Radial Basis Functions

2011 ◽  
Vol 66 (10-11) ◽  
pp. 591-598 ◽  
Author(s):  
Saeed Kazem ◽  
Jamal Amani Rad ◽  
Kourosh Parand ◽  
Saied Abbasbandy
Keyword(s):  
Half Space ◽  
Radial Basis Functions ◽  
Boundary Value ◽  
Basis Functions ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Collocation Points ◽  
Radial Basis ◽  
Grade Fluid ◽  
Porous Half Space

In this study, flow of a third-grade non-Newtonian fluid in a porous half space has been considered. This problem is a nonlinear two-point boundary value problem (BVP) on semi-infinite interval. We find the simple solutions by using collocation points over the almost whole domain [0;∞). Our method based on radial basis functions (RBFs) which are positive definite functions. We applied this method through the integration process on the infinity boundary value and simply satisfy this condition by Gaussian, inverse quadric, and secant hyperbolic RBFs.We compare the results with solution of other methods.

scholarly journals Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier options

2009 ◽  
Vol 29 (2) ◽  
pp. 419-437 ◽  
Author(s):  
Gisele Tessari Santos ◽  
Maurício Cardoso de Souza ◽  
Mauri Fortes
Keyword(s):  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Analytical Solutions ◽  
Financial Engineering ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Barrier Options ◽  
Black Scholes ◽  
Non Linear ◽  
Radial Basis

A large number of financial engineering problems involve non-linear equations with non-linear or time-dependent boundary conditions. Despite available analytical solutions, many classical and modified forms of the well-known Black-Scholes (BS) equation require fast and accurate numerical solutions. This work introduces the radial basis function (RBF) method as applied to the solution of the BS equation with non-linear boundary conditions, related to path-dependent barrier options. Furthermore, the diffusional method for solving advective-diffusive equations is explored as to its effectiveness to solve BS equations. Cubic and Thin-Plate Spline (TPS) radial basis functions were employed and evaluated as to their effectiveness to solve barrier option problems. The numerical results, when compared against analytical solutions, allow affirming that the RBF method is very accurate and easy to be implemented. When the RBF method is applied, the diffusional method leads to the same results as those obtained from the classical formulation of Black-Scholes equation.

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