This paper will use Lagrange parameter in Adomain decomposition method to suggest new method for solving nonlinear differential equation. This method will be highly order convergent. Also, this method will be compared with old existence method. At last, some numerical examples will be given to illustrate the efficiency of newly developed method.

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The researchers are continuously working on nanomaterials and exploring many multidisciplinary applications in thermal engineering, biomedical and industrial systems. In current problem, the analytical simulations for performed for thermos-migration flow of nanofluid subject to the thermal radiation and porous media. The moving wedge endorsed the flow pattern. The heat source effects are also utilized to improves the heat transfer rate. The applications of thermophoresis phenomenon are addressed. The formulated set of expressions are analytically treated with implementation of variational iteration method (VIM). The simulations are verified by making the comparison the numerical date with existing literature. The VIM analytical can effectively tackle the nonlinear coupled flow system effectively. The physical impact for flow regime due to different parameters is highlighted. Moreover, the numerical outcomes are listed for Nusselt number.

The Korteweg-de Vries Burgers (KdVB) is significant in applied mathematics and physical sciences. Particularly, it is a fundamental equation in the study of shallow water waves. The traditional techniques which have been suggested to solve the Korteweg-de Vries Burgers (KdVB) are labor-intensive and time-consuming. The primary goal of this study is to introduce various analytical techniques i.e., Exp-Function Method, Modified Exp-Function Method, Variational Iteration Method, and the Decomposition Method to solve the Korteweg-de Vries Burgers (KdVB) equation. These methods are quickly implemented and give very accurate results of the KdVB equation. Among them, the Variational Iteration Method is particularly user-friendly and simple to implement for the aforementioned problem. The involvement of Lagrange Multiplier is a powerful tool to reduce the cumbersome integration. At the end, Maple18 is used to find the analytical and graphic outcomes. These results show that the proposed methods are effective and applicable to other nonlinear equations of physical interest as well.

One of the major concerns in Flood Frequency Analysis (FFA) is to predict floods of high magnitude for larger return periods. Magnitudes of smaller floods behave as nuisance in the estimation of larger floods. In this study, to avoid the unnecessary effect due to smaller observations, we implemented the technique of left censoring. The primary objective of this study is to see the efficacy of censoring, by comparing Regional Flood Frequency Analysis (RFFA) using Partial Linear Moments (PLM) for censored samples with RFFA using Linear Moments (LM) for uncensored samples of annual peak flows observed at ten stations of Indus Basin in Pakistan. After fulfillment of fundamental assumptions of randomness, independence, homogeneity, and stationarity, a Grubbs-Beck (GB) test for outlier detection is applied to the samples from all stations. For further analysis, Discordancy measure shows that none of the site is discordant and all ten stations would be retained for further investigation. On the basis of geographical closeness, stream hydrology and morphology of Indus basin, a single homogenous region is proposed and testified by the heterogeneity standards. The best fit distribution is selected by implying the Z-statistic (goodness of fit test base on LM) and L-Moments Ratio Diagram (LMRD). Generalized Pareto Distribution (GPA) distribution under PLM while Generalized Normal Distribution (GNO) under LM is selected as the reasonable choice for design flood estimation. Monte Carlo simulation experiment is performed to check the efficacy of PLM over LM through Root Means Square Error (RMSE) and bias. These accuracy measures indicated the outperformance of censored samples under PLM to uncensored samples under LM.