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Fused Filament Fabrication (FFF) is an extrusion-based manufacturing process using fused thermoplastics. Despite its low cost, the FFF is not extensively used in high-value industrial sectors mainly due to parts' anisotropy (related to the deposition strategy) and residual stresses (caused by successive heating cycles). Thus, this study aims to investigate the process improvement and the optimization of the printed parts.

In this work, a meshless technique – the Radial Point Interpolation Method (RPIM) – is used to numerically simulate the viscoplastic extrusion process – the initial phase of the FFF. Unlike the FEM, in meshless methods, there is no pre-established relationship between the nodes so the nodal mesh will not face mesh distortions and the discretization can easily be modified by adding or removing nodes from the initial nodal mesh. The accuracy of the obtained results highlights the importance of using meshless techniques in this field.

Meshless methods show particular relevance in this topic since the nodes can be distributed to match the layer-by-layer growing condition of the printing process.

Using the flow formulation combined with the heat transfer formulation presented here for the first time within an in-house RPIM code, an algorithm is proposed, implemented and validated for benchmark examples.

The numerical methods are of great importance for approximating the solutions of a system of nonlinear singular ordinary differential equations. In this paper, the authors present the biorthogonal flatlet multiwavelet collocation method (BFMCM) as a numerical scheme for a class of system of Lane–Emden equations with initial or boundary or four-point boundary conditions.

The approach is involved in combining the biorthogonal flatlet multiwavelet (BFM) with the collocation method. The authors investigate the properties and procedure of the BFMCM for first time on this class of equations. By using the BFM and the collocation points, the method is constructed and it transforms the nonlinear differential equations problem into a system of nonlinear algebraic equations. The unknown coefficients of the assuming solution are determined by solving the obtained system. Additionally, convergence analysis and numerical stability of the suggested method are provided.

According to the attained results, the proposed BFMCM has more accurate results in comparison with results of other methods. The maximum absolute errors are calculated by using the BFMCM for comparison purposes provided.

The key desirable properties of BFMCM are its efficiency, simple applicability and minimizes errors. Therefore, the proposed method can be used to solve nonlinear problems or problems with singular points.

This article offered two meshfree algorithms, namely the local radial basis functions-finite difference (LRBF-FD) approximation and local radial basis functions-differential quadrature method (LRBF-DQM) to simulate the multidimensional hyperbolic wave models and work is an extension of Jiwari (2015).

In the evolvement of the first algorithm, the time derivative is discretized by the forward FD scheme and the Crank-Nicolson scheme is used for the rest of the terms. After that, the LRBF-FD approximation is used for spatial discretization and quasi-linearization process for linearization of the problem. Finally, the obtained linear system is solved by the LU decomposition method. In the development of the second algorithm, semi-discretization in space is done via LRBF-DQM and then an explicit RK4 is used for fully discretization in time.

For simulation purposes, some 1D and 2D wave models are pondered to instigate the chastity and competence of the developed algorithms.

The developed algorithms are novel for the multidimensional hyperbolic wave models. Also, the stability analysis of the second algorithm is a new work for these types of model.

This study aimed to examine the efficient market hypothesis (EMH) for the stock markets of 12 member countries of the Organization of Islamic Cooperation (OIC), such as Egypt, Indonesia, Jordan, Kuwait, Malaysia, Morocco, Pakistan, Saudi Arabia, Tunisia, Turkey and the United Arab Emirates (UAE), during the global financial crisis (GFC) and the COVID-19 (CV-19) epidemic. The objective was to classify the effects on individual indices.

The study employed the multifractal detrended fluctuation analysis (MF-DFA) on daily returns. After calculation and analysis, the data were then divided into two significant events: the GFC and the CV-19 pandemic. Additionally, the market deficiency measure (MDM) was utilized to assess and rank market efficiency.

The findings indicate that the average returns series exhibited persistent and non-persistent patterns during the GFC and the CV-19 pandemic, respectively. The study employed MF-DFA to analyze the sequence of normal returns. The results suggest that the average returns series displayed persistent and non-persistent patterns during the GFC and the CV-19 pandemic, respectively. Furthermore, all markets demonstrated efficiency during the two crisis periods, with Turkey and Tunisia exhibiting the highest and deepest levels of efficiency, respectively. The multifractal properties were influenced by long-range correlations and fat-tailed distributions, with the latter being the primary contributor. Moreover, the impact of the fat-tailed distribution on multifractality was found to be more pronounced for indices with lower market efficiency. In conclusion, this study categorizes indices with low market efficiency during both crisis periods, which subsequently affect the distribution of assets among shareholders in the stock markets of OIC member countries.

Multifractal patterns, especially the long memory property observed in stock markets, can assist investors in formulating profitable investment strategies. Additionally, this study will contribute to a better understanding of market trends during similar events should they occur in the future.

This research marks the initial effort to assess the impact of the GFC and the CV19 pandemic on the efficiency of stock markets in OIC countries. This undertaking is of paramount importance due to the potential destabilizing and harmful effects of these events on global financial markets and societal well-being. Furthermore, to the best of the authors’ knowledge, this study represents the first investigation utilizing the MFDFA method to analyze the primary stock markets of OIC countries, encompassing both the GFC and CV19 crises.

The space fractional PDEs (SFPDEs) play an important role in the fractional calculus field. Proposing a high-order, stable and flexible numerical procedure for solving SFPDEs is the main aim of most researchers. This paper devotes to developing a novel spectral algorithm to solve the FitzHugh–Nagumo models with space fractional derivatives.

The fractional derivative is defined based upon the Riesz derivative. First, a second-order finite difference formulation is used to approximate the time derivative. Then, the Jacobi spectral collocation method is employed to discrete the spatial variables. On the other hand, authors assume that the approximate solution is a linear combination of special polynomials which are obtained from the Jacobi polynomials, and also there exists Riesz fractional derivative based on the Jacobi polynomials. Also, a reduced order plan, such as proper orthogonal decomposition (POD) method, has been utilized.

A fast high-order numerical method to decrease the elapsed CPU time has been constructed for solving systems of space fractional PDEs.

The spectral collocation method is combined with the POD idea to solve the system of space-fractional PDEs. The numerical results are acceptable and efficient for the main mathematical model.