A Numerical Approach for Solving Quadratic Integral Equations of Urysohn’s Type using Radial Basis Function

A Numerical Approach for Solving Quadratic Integral Equations of Urysohn’s Type using Radial Basis Function

Introduction Quadratic integral equations provide an important tool for modeling the numerous problems in engineering and science. These equations appear in the modeling of radiative transfer, kinetic theory of gases, traffic theory, neutron transport and in many other phenomena [2-7]. So, it is clear that solving this class of integral equations can be used to describe many events in the real ...

Stable Gaussian radial basis function method for solving Helmholtz equations

‎Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems‎. ‎They are often referred to as a meshfree method and can be spectrally accurate‎. ‎In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion‎. ‎We develop our approach in two-dimensional spaces for so...

Numerical ‎S‎olution of Two-Dimensional Hyperbolic Equations with Nonlocal Integral Conditions Using Radial Basis Functions‎

This paper proposes a numerical method to the two-dimensional hyperbolic equations with nonlocal integral conditions. The nonlocal integral equation is of major challenge in the frame work of the numerical solutions of PDEs. The method benefits from collocation radial basis function method, the generalized thin plate splines radial basis functions are used.Therefore, it does not require any str...

Numerical Solution of Singular IVPs of Lane-Emden Type Using Integral Operator and Radial Basis Functions

A Numerical Approach for Solving of Two-Dimensional Linear Fredholm Integral Equations with Boubaker Polynomial Bases

In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...