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In this paper, the generalized differential transform method (GDTM) is used to solve certain class of nonlinear time-fractional diffusion equation. An efficient recurrence relation is obtained to solve this problem. Some numerical examples are given for different class of derivative orders which are analyzed numerically for the specified examples. [ABSTRACT FROM AUTHOR]

In this paper, a numerical approach for solving space-time fractional diffusion equation with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind. The space-time fractional diffusion equation with variable coefficients is reduced to a system of ordinary differential equations by using the properties of Chebyshev polynomials. The finite difference method is applied to solve this system of equations. Numerical results are provided to verify the accuracy and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the author considers the one dimensional initial-boundary problem for a pseudo-parabolic equation with time delay in second spatial derivative. To solve this problem numerically, the author constructs higher order difference method and obtain the error estimate for its solution. Based on the method of energy estimates the fully discrete scheme is shown to be convergent of order four in space and of order two in time. Some numerical examples illustrate the convergence and effectiveness of the numerical method. [ABSTRACT FROM AUTHOR]

The paper deals with problem on asymptotic solutions to a system of singular perturbed linear differential-algebraic equations. Case of multiple roots of a characteristic equation is studied. Technique of constructing the asymptotic solutions is developed. [ABSTRACT FROM AUTHOR]

In this paper we consider a problem for the first order Dirac differential equations system with spectral parameter dependent on boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this system are investigated. The expansion formula with respect to eigenfunctions is obtained and Parseval equality is given. The main theorem on necessary and sufficient conditions for the solvability of inverse problem is proved and the algorithm of reconstruction of potential from spectral data (the sets of eigenvalues and normalizing numbers) is given. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of eventually positive (negative) and oscillatory solutions to the following nonhomogeneous second order delay differential equation ... where p and f are suitable real functions. [ABSTRACT FROM AUTHOR]

In the last two decades, substantial effort has been devoted to solve large systems of linear equations with algebraic multigrid (AMG) method. Usually, these systems arise from discretizing partial differential equations (PDE) which we encounter in engineering problems. The main principle of this methodology focuses on the elimination of the so-called algebraic smooth error after the smoother has been applied. Smoothed aggregation style multigrid is a particular class of AMG method whose coarsening process differs from the classic AMG. It is also a very popular and effective iterative solver and preconditioner for many problems. In this paper, we present two kinds of novel methods which both focus on the modification of the aggregation algorithm, and both lead a better performance while apply to several problems, such as Helmholtz equation. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new integral inequalities for convex and m–convex functions by using a new kernel. The analysis used in the proofs is fairly elementary and based on the classical inequalities. We also give some comparisons and applications to special means for our results. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to derive a new inequality of Ostrowski-Grüss type with a parameter involving functions of two independent variables. [ABSTRACT FROM AUTHOR]

In this paper, we prove endpoint boundedness of multilinear commutators of Littlewood-Paley operators. [ABSTRACT FROM AUTHOR]