We determine a decomposition of the solution fractional difference initial-value problem with periodic right-hand side. For problems S-asymptotically N-periodic side, sufficient condition is proved for existence an solution.

The global FOM and GMRES are among the effective algorithms to solve linear system of equations with multiple right-hand sides. In this paper, we study these algorithms in the case that the coefficient matrix is symmetric and extract two CGtype algorithms for solving symmetric linear systems of equations with multiple right– hand sides. Then, we compare the numerical performance of the new algo...

In this work, we discuss some theoretical and numerical aspects of solving differential equations with discontinuous right-hand sides of Filippov type. In particular: (i) we propose second order corrections to the theory of Filippov, (ii) we provide a systematic and non-ambiguous way to define the vector field on the intersection of several surfaces of discontinuity, and (iii) we propose, and i...

Some three-dimensional analogues of the plane Darboux problems for hyperbolic equations with degeneracy are investigated. In 1954, Protter initiated the study of such threedimensional problems, and it is now well known that for an infinite number of smooth right-hand sides these problems have solutions with a strong power-type singularity on the characteristic cone. This effect appears even for...