In this paper, the authors study the forward and inverse problems for a fractional boundary value problem with Dirichlet boundary conditions. The existence and uniqueness of solutions for the forward problem is first proved. Then an inverse source problem is considered. [ABSTRACT FROM AUTHOR]
*COMPUTER simulation, *EIGENVALUES, *DIRAC function, *DISCONTINUOUS functions, *PARAMETER estimation, *NUMERICAL analysis, *BOUNDARY value problems, *ERROR analysis in mathematics
Abstract
In this paper, we apply a regularized sinc method to compute the eigenvalues of a discontinuous regular Dirac system with transmission conditions at the point of discontinuity. The regularized technique allows us to insert some parameters to the well-known sinc method, strengthening the existing technique, and to avoid the aliasing error. The error analysis is established considering both the truncation and amplitude errors associated with the sampling theorem. Numerical examples together with tables and illustrative figures are given. [ABSTRACT FROM PUBLISHER]
In this paper, we construct a group of Saul'yev type asymmetric difference formulas for the dispersive equation. Based on these formulas we derive a new alternating 6-point group algorithm to solve dispersive equations with periodic boundary conditions. The algorithm has a high-order accuracy in space and an unconditional stability. The theoretical results are conformed to the numerical simulation. A comparison of this algorithm with the previous Alternating Group Explicit method is presented. [ABSTRACT FROM AUTHOR]