Point-wise Integrated-RBF-based Discretisation of Differential Equations
نویسندگان
چکیده
This paper discusses a discretisation scheme which is based on point collocation and integrated radial basis function networks (IRBFNs) for the solution of elliptic differential equations (DEs). The use of IRBFNs to represent the field variable in a given DE gives several advantages over the case of using conventional RBFNs and polynomials. Some numerical examples are included for demonstration purposes.
منابع مشابه
Compact local integrated-RBF approximations for second-order elliptic differential problems
This paper presents a new compact approximation method for the discretisation of second-order elliptic equations in one and two dimensions. The problem domain, which can be rectangular or non-rectangular, is represented by a Cartesian grid. On stencils, which are three nodal points for one-dimensional problems and nine nodal points for twodimensional problems, the approximations for the field v...
متن کاملFinite integration method for solving multi-dimensional partial differential equations
Based on the recently developed Finite Integration Method (FIM) for solving one-dimensional ordinary and partial differential equations, this paper extends the technique to higher dimensional partial differential equations. The main idea is to extend the first order finite integration matrices constructed by using either Ordinary Linear Approach (OLA) (uniform distribution of nodes) or Radial B...
متن کاملA Method for Solving Convex Quadratic Programming Problems Based on Differential-algebraic equations
In this paper, a new model based on differential-algebraic equations(DAEs) for solving convex quadratic programming(CQP) problems is proposed. It is proved that the new approach is guaranteed to generate optimal solutions for this class of optimization problems. This paper also shows that the conventional interior point methods for solving (CQP) problems can be viewed as a special case of the n...
متن کاملFree vibration analysis of thin annular plates integrated with piezoelectric layers using differential quadrature method
In this article, using generalized differential quadrature (GDQ) methods, free vibration of a thin annular plate coupled with two open circuit piezoelectric layers, is numerically studied based on the classical plate theory. The governing differential equations with respective boundary conditions are derived and transformed into a set of algebraic equations by implementing the GDQ rule, then so...
متن کاملRBF-PS method and Fourier Pseudospectral method for solving stiff nonlinear partial differential equations
Radial basis function-Pseudospectral method and Fourier Pseudospectral (FPS) method are extended for stiff nonlinear partial differential equations with a particular emphasis on the comparison of the two methods. Fourth-order Runge-Kutta scheme is applied for temporal discretization. The numerical results indicate that RBF-PS method can be more accurate than standard Fourier pseudospectral meth...
متن کامل