This paper evaluates the performances of Perturbation Methods, the Parameterized Expectations Algorithm and Projection Methods in finding approximate decision rules of the basic neoclassical stochastic growth model. In contrast to the existing literature, we focus on comparing numerical methods for a given functional form of the approximate decision rules, and we repeat the evaluation for many ...

This work introduces a new perturbation bound for the L factor of the LDU factorization of (row) diagonally dominant matrices computed via the column diagonal dominance pivoting strategy. This strategy yields L and U factors which are always well-conditioned and, so, the LDU factorization is guaranteed to be a rank-revealing decomposition. The new bound together with those for the D and U facto...

Nuclear scales are discussed from the nuclear physics viewpoint. The conventional nuclear potential is characterized as a black box that interpolates nucleon-nucleon (NN) data, while being constrained by the best possible theoretical input. The latter consists of the longer-range parts of the NN force (e.g., OPEP, TPEP, the π-γ force), which can be calculated using chiral perturbation theory an...

The rapid and robust simulation of linear waves interacting with layered periodic media is a crucial capability in many areas of scientific and engineering interest. High-order perturbation of surfaces (HOPS) algorithms are interfacial methods which recursively estimate scattering quantities via perturbation in the interface shape heights/slopes. For a single incidence wavelength such methods a...

We investigate the Benjamin-Feir (or modulational) instability of Stokes waves, i.e., small-amplitude, one-dimensional periodic gravity waves permanent form and constant velocity, in water finite infinite depth. develop a perturbation method to describe high-order accuracy unstable spectral elements associated with this instability, obtained by linearizing Euler's equations about small-amplitud...

in this paper, we present an ecient numerical algorithm for solving fuzzy systemsof linear equations based on homotopy perturbation method. the method is discussed indetail and illustrated by solving some numerical examples.

We present an extension to the gauge-invariant formulation of parameterized post-Newtonian (PPN) formalism, which allows its application symmetric teleparallel gravity theories. In original formulation, PPN formalism makes use a perturbative expansion tensor fields; however, one fundamental gravitational field variables in theories is flat, torsion-free connection, hence not field. Since connec...

More recently, Wazwaz [An analytic study of Fisher’s equation by using Adomian decomposition method, Appl. Math. Comput. 154 (2004) 609–620] employed the Adomian decomposition method (ADM) to obtain exact solutions to Fisher’s equation and to a nonlinear diffusion equation of the Fisher type. In this paper, He’s homotopy perturbation method is employed for the generalized Fisher’s equation to o...

In this paper, He’s homotopy perturbation method is applied to solve linear Schrodinger equation. The method yields solutions in convergent series forms with easily computable terms. The result show that these method is very convenient and can be applied to large class of problems. Some numerical examples are given to effectiveness of the method.

Inthispaper,wesolveHamilton-Jocobi-Bellman(HJB)equationsarisinginoptimalcontrolproblems usingHomotopyPerturbationTransformMethod(HPTM).Theproposedmethodisacombinedform oftheLaplaceTransformationMethodwiththeHomotopyPerturbationMethodtoproduceahighly effectivemethodtohandlemanyproblems. ApplyingtheHPTM,solutionprocedurebecomeseasier, simplerandmorestraightforward. Someillustrativeexamplesaregive...