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Analytical approximate solutions for the nonlinear oscillators of the form are derived using the modified decomposition method. The analytical solutions of our model equations are calculated in the form of convergent series with easily computable components. Then the Laplace transformation and Padè approximant are effectively used to improve the convergence rate and accuracy of the computed series. The validity of the solutions is verified through some numerical examples. The results compare well with those obtained by the Runge–Kutta fourth-order method. The proposed scheme avoids the complexity provided by perturbation techniques.

Surrogate data methods have been widely applied to produce synthetic data, while maintaining the same statistical properties as the original. By using such methods, one can analyze certain properties of time series. In this context, Theiler's surrogate data methods are the most commonly considered approaches. These are based on the Fourier transform, limiting them to be applied only on stationary time series. Consequently, time series including nonstationary behavior, such as trend, produces spurious high frequencies with Theiler's methods, resulting in inconsistent surrogates. To solve this problem, we present two new methods that combine time series decomposition techniques and surrogate data methods. These new methods initially decompose time series into a set of monocomponents and the trend. Afterwards, traditional surrogate methods are applied on those individual monocomponents and a set of surrogates is obtained. Finally, all individual surrogates plus the trend signal are combined in order to create a single surrogate series. Using this method, one can investigate linear and nonlinear Gaussian processes in time series, irrespective of the presence of nonstationary behavior.

This paper is devoted to investigating or computing the solution to one-dimensional partial fuzzy fractional order heat equation. In particular, one-dimensional fuzzy partial heat equation is hybridized into two equations by hybrid techniques along with the concept of parametric fuzzy number. For this investigation, a hybrid method of decomposition due to Adomian and Laplace transform is used. The considered techniques are presented for the computation of series of solutions of partial fractional order heat equation. The applied techniques have also provided the accuracy, simplicity and efficiency as compared to other existing methods. Finally, some illustrations are solved for the justification of our theoretical solution.

In this paper, we first propose a method, which is originated from coupling local fractional Yang–Laplace transform with the Daftardar–Gejji–Jafaris method (LFYLTDGJM). The proposed method is successfully applied to solve the local time fractional nonlinear modified Korteweg–de Vries (TFNMKDV) equation. The approximate solution presented here illustrates the efficiency and accuracy of the proposed computational technique to solve fractional nonlinear the partial differential equations involving local fractional operators.

To approximately calculate the line throughput and the average level of each buffer for a continuous type transfer line L, Dallery⁴ proposed an iterative algorithm when L is homogeneous (i.e., all its machines have an identical production rate). Non-homogeneous L needs to be transformed into a homogeneous one first in order that such a method can be applicable. The purpose of this article is to extend Dallery’s algorithm so that it also holds for any non-homogeneous L without such a transformation, simply by replacing two sets of equations in Ref. 4 by more general ones. Numerical examples are presented. Comparisons with both simulation and homogenization results in Ref. 4 are provided. In particular, the numerical results of the line throughput by our method are very close to those of the simulation.

Firm-level data spanning from 1994 to 2012 is used to investigate the apparent stagnation of Mexican microenterprises. The existence and nature of constraints are studied by estimating the empirical probability of a business’s success. A performance index is defined based on firm levels of capital stock and monthly profits. The predicted values are used to classify all microenterprises into one of three categories: upper, middle, or lower segment. Overall, the study identifies evidence of constrained productivity and capital misallocation, as well as the plausibility of cost-effective interventions. Specifically, microenterprises from the middle segment face substantial external constraints and their total share increased from 16 to 22 percent over time. The monthly marginal returns average 30 percent across lower-segment firms and 1 percent across those in the upper segment. Finally, the differences in monthly profits among segments are explored using the Oaxaca-Blinder decomposition method.

In this paper, we find the solutions for two-dimensional biological population model having fractional order using fractional natural decomposition method (FNDM). The proposed method is a graceful blend of decomposition scheme with natural transform, and three examples are considered to validate and illustrate its efficiency. The nature of FNDM solution has been captured for distinct arbitrary order. In order to illustrate the proficiency and reliability of the considered scheme, the numerical simulation has been presented. The obtained results illuminate that the considered method is easy to apply and more effective to examine the nature of multi-dimensional differential equations of fractional order arisen in connected areas of science and technology.

One-factor term structure model in finance and economic setups conveys the opinion that there exists only one Brownian process in the formulation of the short rate model as one source of randomness. To extend the theory, in this paper, we develop the approximate solution of a one-factor bond pricing model that can be used to obtain solutions of both nonlinear and multi-factor models and get applications of two proposed solution methods: Elzaki Adomian decomposition method (EADM) and Laplace Adomian decomposition solution method (LADM). We first obtain an efficient, reliable and approximate-analytical solution for a one-factor bond pricing model. We provide illustrative examples that are in good agreement when compared with those already in literature. The methods are very effective in the application being the modified version of the classical Elzaki, and Laplace transforms. Since our proposed methods are effective and efficient, we recommend academics and practitioners apply our proposed model to obtain solutions for some financial models, including both the multi-factor and nonlinear models.