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This chapter is mainly a tutorial introduction to methods recently developed in order to find all (as opposed to some) meromorphic particular solutions of given nonintegrable, autonomous, algebraic ordinary differential equations of any…

Exactly Solvable and Integrable Systems · Physics 2018-06-11 Robert Conte , Tuen Wai Ng , Chengfa Wu

A simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a Hamiltonian H with singular potentials. Closed-form analytic expressions in N dimensions are obtained for the matrix…

Mathematical Physics · Physics 2009-11-10 Nasser Saad , Richard L. Hall , Qutaibeh D. Katatbeh

We approximately solve the Dirac equation for the inversely quadratic Yukawa (IQY) potential including a Coulomb-like tensor potential with arbitrary spin-orbit coupling quantum number . In the framework of the spin and pseudospin (pspin)…

Quantum Physics · Physics 2012-04-02 Majid Hamzavi , Sameer M. Ikhdair , B. I. Ita

The prime objective of this paper is to design a new family of eighth-order iterative methods by accelerating the order of convergence and efficiency index of well existing seventh-order iterative method of \cite{Soleymani1} without using…

Numerical Analysis · Mathematics 2014-03-28 Anuradha Singh , J. P. Jaiswal

Efficient solvers for tensor eigenvalue problems are important tools for the analysis of higher-order data sets. Here we introduce, analyze and demonstrate an extrapolation method to accelerate the widely used shifted symmetric higher order…

Numerical Analysis · Mathematics 2023-07-25 Sara Pollock , Rhea Shroff

It is shown that a generalization of the Painlev\'e-II equation (P-II) to a system of coupled equations with symmetry breaking terms is integrable. A Lax pair for this system is used to relate the asymptotic behavior of the solutions at…

Mathematical Physics · Physics 2026-03-30 N. A. Sinitsyn

In this work we show how auxiliary variables can be used to give an efficient method involving symbolic manipulation and Picard iteration for approximating solutions of certain Volterra integral equations.

Classical Analysis and ODEs · Mathematics 2016-11-15 Hamid Semiyari , Douglas Shafer

In this paper the asymptotic distributions are exactly solved for linearly independent solutions considering problems of the second order and for the coefficients of asymptotic destribution the recurent formulas are obtained. Further, using…

Mathematical Physics · Physics 2007-05-23 Yu. A. Mamedov , H. I. Ahmadov

The approximate analytical bound state solution of the Schr\"odinger equation for the Manning-Rosen potential is carried out by taking a new approximation scheme to the orbital centrifugal term. The Nikiforov-Uvarov method is used in the…

Quantum Physics · Physics 2012-03-14 Sameer M. Ikhdair

We examine some numerical iterative methods for computing the eigenvalues and eigenvectors of real matrices. The five methods examined here range from the simple power iteration method to the more complicated QR iteration method. The…

Numerical Analysis · Mathematics 2011-05-09 Maysum Panju

In this paper we consider the locally backward self-similar solutions for the Euler system, and focus on the case that the possible nontrivial velocity profiles have non-decaying asymptotics. We derive the meaningful representation formula…

Analysis of PDEs · Mathematics 2015-02-09 Liutang Xue

In this paper, an inexact Newton method for solving real-valued nonlinear eigenvalue problems with eigenvector dependency (NEPv) is introduced that is able to solve the problem on a matrix level. Our main contribution is to derive a variant…

Numerical Analysis · Mathematics 2024-09-04 Tom Werner

By using the Pekeris approximation, the Schrodinger equation is approximately solved for the nuclear deformed Woods-Saxon potential within the framework of the asymptotic iteration method. The energy levels are worked out and the…

Nuclear Theory · Physics 2013-01-04 Babatunde J. Falaye , Majid Hamzavi , Sameer M. Ikhdair

The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…

Numerical Analysis · Mathematics 2013-09-24 Anuradha Singh , J. P. Jaiswa

This paper investigates the dynamical behavior of periodic solutions for a class of second-order non-autonomous differential equations. First, based on the Lyapunov-Schmidt reduction method for finite-dimensional functions, the…

Classical Analysis and ODEs · Mathematics 2025-04-03 Jia Ruan

Two approaches for approximating the solution of large-scale Lyapunov equations are considered: the alternating direction implicit (ADI) iteration and projective methods by Krylov subspaces. A link between them is presented by showing that…

Numerical Analysis · Mathematics 2014-02-13 Thomas Wolf , Heiko K. F. Panzer

This paper reports on a new algorithm to compute the asymptotic solutions of a linear differential system. A feature of the algorithm is the ability to accommodate periodic coefficients.

Spectral Theory · Mathematics 2025-10-20 B. M. Brown , M. S. P. Eastham , D. K. R. McCormack

An alternative treatment is proposed for the calculations carried out within the frame of Nikiforov-Uvarov method, which removes a drawback in the original theory and by pass some difficulties in solving the Schrodinger equation. The…

Quantum Physics · Physics 2007-05-23 B. Gonul , K. Koksal

By using generalized fractional derivative, the parametric generalized fractional Nikiforov-Uvarov (NU) method is introduced. The second-order parametric generalized differential equation is exactly solved in the fractional form. The…

Quantum Physics · Physics 2023-09-06 M. Abu-shady , H. M. Fath-Allah

Asymptotic formula is derived for the behavior of the fundamental solution of the second-order elliptic self-adjoint operator with a piecewise-smooth coefficient in front of the senior derivatives near the discontinuity surface of the…

Mathematical Physics · Physics 2007-05-23 A. G. Ramm