Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
نویسنده
چکیده
Fractional powers of linear multistep methods are suggested for the numerical solution of weakly singular Volterra integral equations. The proposed methods are convergent of the order of the underlying multistep method, also in the generic case of solutions which are not smooth at the origin. The stability properties (stability region, A-stability, A(a)-stability) are closely related to those of the underlying linear multistep method.
منابع مشابه
The solving linear one-dimemsional Volterra integral equations of the second kind in reproducing kernel space
In this paper, to solve a linear one-dimensional Volterra integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of integral equation in terms of the basis functions. The examples presented in this ...
متن کاملNUMERICAL SOLUTION OF LINEAR FREDHOLM AND VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND BY USING LEGENDRE WAVELETS
In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...
متن کاملFuzzy collocation methods for second- order fuzzy Abel-Volterra integro-differential equations
In this paper we intend to offer new numerical methods to solve the second-order fuzzy Abel-Volterraintegro-differential equations under the generalized $H$-differentiability. The existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.
متن کاملSolving Volterra Integral Equations of the Second Kind with Convolution Kernel
In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad et al., [K. Maleknejad and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, Appl. Math. Comput. (2005)] to gain...
متن کامل