Статьи

The objective of this paper is to construct a generalized quadratic spectrum approximation based on the Kantorovich projection method which llows us to deal with the spectral pollution problem. For this purpose, we prove that the property U (see Eq. 3) holds under weaker conditions than the norm and the collectively compact convergence. Numerical results illustrate the effectiveness and the convergence of our method.

We compare the error behavior of two methods used to find a numerical solution of the linear integro-differential Fredholm equation with a weakly singular kernel in Banach space C1[a,b]. We construct an approximation solution based on the modified cubic b-spline collocation method. Another estimation of the exact solution, constructed by applying the numerical process of product and quadrature integration, is considered as well. Two proposed methods lead to solving a linear algebraic system. The stability and convergence of the cubic b-spline collocation estimate is proved. We test these methods on the concrete examples and compare the numerical results with the exact solution to show the efficiency and simplicity of the modified collocation method.