Numerical Solution Methods Of Several Types Of Integral Equations Based On Radial Basis Function

Integral equation is known as the forerunner of linear algebra,and is also a very im-portant branch of modern mathematics.Many problems in fields such as neural networks,fracture mechanics,physical engineering,etc.,are ultimately reduced to solving integral e-quation.However,it is a pity that the analytic solution is difficult to be obtained for this kind of equation.Even if the analytic solution is obtained,the complex form of the solution is difficult to be generalized and applied in practical problems.So,the numerical solution of integral equation has become a hot topic,especially the numerical solution of the second type Fredholm integral(differential)equations.Therefore,three kinds of linear integral equations are solved numerically based on the radial basis function(RBF)interpolation collocation method.This paper first introduces the concept of RBF?property conditions and interpola-tion principle,Legendre-Gauss-Lobatto(L-G-L)quadrature formula.Secondly,the numer-ical discretization schemes of the second type of linear Fredholm integral equations,lin-ear Volterra-Fredholm integral equations and first-order linear Fredholm(Volterra)integro-differential equations are derived,the existence and uniqueness of the solutions are proved,and the convergence and error estimation of the numerical solutions are analyzed.Finally,a numerical example with L2 norm?L? norm?absolute error ? and root mean square error(RMS)depict the error between the numerical and analytical solutions,and the method of this paper the method of literature and the comparison of numerical results in detail,found that the present numerical results accuracy is higher than the literature accuracy of numerical results,which proves the validity and feasibility of this method.