In this paper, we reduce the 1-D, 2-D and 3-D inverse scattering problems of the wave equation into the nonlinear integral equation. The iteration for solving the above integral equations has been considered.

In this paper, an iterative algorithm for solving a coefficient inverse problem is submitted. The key of the method is to project an unknown coefficient function on a finite dimensional function space. Thus, the inverse problem can be changed into a nonlinear algebraic system of equations.

In this paper we investigate the attainable order of convergence of collocation approximations in certain polynomial spline spaces for solutions of a class of second-order volterra integro-differential equations with weakly singular kernels. While the use of quasi-uniform meshes leads, due to the nonsmooth nature of these solutions, to convergence of order less than one, regardless of the degree of the approximating spling function, collocation on suitably graded meshes will be shown to yield optimal convergence rates.

In the presence of reentrant corners or changing boundary conditions, standard finite element schemes have only a reduced order of accuracy even at interior nodal points. This pollution effect can be completely described in terms of asymptotic expansions of the error with respect to certain fractional powers of the mesh size. Hence, eliminating the leading pollution terms by Richardson extrapolation may locally increase the accuracy of the scheme. It is shown here that this approach also gives improved approximations for eigenvalues and eigenfunctions which are globally defined quantities.

There are several methods for solving operator equations in a Banach space. The successive approximation methods require the spectral radius of the iterative operator be less that 1 for convergence.
In this paper, we try to use the incomplete semiiterative methods to solve a linear operator equation in Banach space. Usually the special semiiterative methods are convergent even when the spectral radius of the iterative operator of an operator of an operator equation is greater than 1.  

For a certain kind of multivariate Padé approximation problems, we establish in this paper some results about the solvability and uniqueness of its solution. We also give the necessary and sufficient conditions for the continuity of Padé approximation operator. The application of such approximations in finding solutions of systems of nonlinear equations is considered, and some numerical examples are given, in which it is shown that the Padé methods are more effective than the Newton methods in some cases.

This paper deals with a system of ordinary differential equations with known conditions associated with a given matrix. By using analytical and computational methods, the generalized inverses of the given matrix can be determined. Among these are the weighted Moore-Penrose inverse, the Moore-Penrose inverse, the Drazin inverse and the group inverse. In particular, a new insight is provided into the finite algorithms for computing the generalized inverse and the inverse.

We present a non-conforming domain decomposition technique for solving elliptic problems with the finite element method. Functions in the finite element space associated with this method may be discontinuous on the boundary of subdomains. The sizes of the finite meshes, the kinds of elements and the kinds of interpolation functions may be different in different subdomains. So, this method is more convenient and more efficient than the conforming domain decomposition method. We prove that the solution obtained by this method has the same convergence rate as by the conforming method, and both the condition number and the order of the capacitance matrix are much lower than those in the conforming case.

In this paper, we present some results of a study, specifically within the framework of symplectic geometry, of difference schemes for numerical solution of the linear Hamiltonian systems. We generalize the Cayley transform with which we can get different types of symplectic schemes. These schemes are various generalizations of the Euler centered scheme. They preserve all the invariant first integrals of the linear Hamiltonian systems.

This paper discussed the number of zeros of the complex function $F:C \rightarrow C$ defined by $$F(Z)=\sum\limits_{k=1}^n(a_k cos(kZ)+b_k sin(kZ))+α_0+α_1 Im(z)+\cdots+α_m(Im(Z))^m.$$