Power series techniques for a special Schrödinger operator and related difference equations

Special formal series solutions of linear operator equations

The transformation which assigns to a linear operator L the recurrence satis ed by coe cient se quences of the polynomial series in its kernel is shown to be an isomorphism of the corresponding operator algebras We use this fact to help factoring q di erence and recurrence operators and to nd nice power series solutions of linear di erential equations In particular we characterize generalized h...

A Fuzzy Power Series Method for Solving Fuzzy Differential Equations With Fractional Order

In this paper a new method for solving fuzzy differential equation with fractional order is considered. The fuzzy solution is construct by power series in the Caputo derivatives sense. To illustrate the reliability of method some examples are provided. In this paper a new method for solving fuzzy differential equation with fractional order is considered. The fuzzy solution is construct by power...

‎A matrix LSQR algorithm for solving constrained linear operator equations

In this work‎, ‎an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $mathcal{A}(X)=B$‎ ‎and the minimum Frobenius norm residual problem $||mathcal{A}(X)-B||_F$‎ ‎where $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$‎, ‎$mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$‎, ‎$ma...

Hypergeometric series solutions of linear operator equations

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...