this paper presents an approach for solving a nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices areused for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of equations and unknowns. then, the error anal...

this article proposes a direct method for solving three types of integral equations with time delay. by using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. numerical examples shows that the proposed scheme have a suitable degree of accuracy.

Total Least Squares (TLS) is a method for treating an overdetermined system of linear equations Ax ≈ b, where both the matrix A and the vector b are contaminated by noise. In practical situations, the linear system is often ill-conditioned. For example, this happens when the system is obtained via discretization of ill-posed problems such as integral equations of the first kind (see e.g., [7] a...

We consider the problem of reconstructing frames from a video which has been compressed using the video compressive sensing (VCS) method. In VCS data, each frame comes from first subsampling the original video data in space and then averaging the subsampled sequence in time. This results in a large linear system of equations whose inversion is ill-posed. We introduce a convex regularizer to inv...

A new method due to Fokas for explicitly solving boundary-value problems for linear partial differential equations is extended to equations with mixed partial derivatives. The Benjamin-Bona-Mahony equation is used as an example: we consider the Robin problem for this equation posed both on the half line and on the finite interval. For specific cases of the Robin boundary conditions the boundary...