Previous numerical methods for solving systems of higher order ordinary differential equations (ODEs) directly require calculating the integration coefficients at every step. This research provides a block multi step method for solving orbital problems with periodic solutions in the form of higher order ODEs directly. The advantage of the proposed method is, it requires calculating the integration coefficients only once at the beginning of the integration is presented. The derived formulae is then validated by running simulations with known higher order orbital equations. To provide further efficiency, a relationship between integration coefficients of various order is obtained.

ABSTRCKHalal violation is a critical issue in the Islamic market, but little is known on its impact on the Muslim consumer. Thus, this study investigates the effect of psychological contract violation (PCV), recovery satisfaction, and severity of halal violation on product boycott. The moderating role of PCV in the relationship between recovery satisfaction and seriousness of a violation on the product boycott is also examined. Data collected from a sample of 360 customers were analyzed using PLS-SEM. The results show that recovery satisfaction, severity, and PCV significantly influence product boycott and PCV significantly moderates the relationship between recovery satisfaction and product boycott. This study provides new insights into the relationships among recovery satisfaction, the severity of the halal violation, psychological contract violation, and product boycott and helps the managers to design recovery action toward halal violation.

Purpose - Managing trust recovery in case of violation of halal products should be seen in light of the severity of violation as perceived by the consumer. This study aims to investigate how the severity of violation on halal directly impact negative consumer behavior (avoidance, boycott and revenge), and its moderating effect on the relationship between trust recovery and avoidance, boycott and revenge. Design/methodology/approach - In total, 212 questionnaires were distributed amongst customers who were aware and/or had experienced the violation of a halal product in Klang Valley, Malaysia - each of whom were selected using convenience sampling methods. Data were analyzed using descriptive statistics and structural equation modelling techniques, were partial least squares (PLS) software was used to measure the direct and indirect relationships between the variables. Findings - The results of this investigation showed that trust recovery and negative consumer behavior are negatively related; severity is positively related to avoidance, boycott and revenge; and severity moderates the relationship between trust recovery and avoidance. Research limitations/implications - Empirically, it was found that severity and trust recovery are a significant component that influence negative consumption behavior. This study has significant implications alongside research implications despite some limitations. Practical implications - In a severe violation case, a company needs to ensure that the strategy to fix the problem is genuine and trustworthy, as consumer trust on the recovery action by company is significance to influence customer avoidance in consuming the company's product. Originality/value - The uniqueness of this study exists in the fact that it is the first known one to concentrate on halal violation and examine the moderating effect of severity of halal violation on the relationship between trust recovery and negative consumer behaviors (avoidance, boycott and revenge).

Real life phenomena found in various fields such as engineering, physics, biology and communication theory can be modeled as nonlinear higher order ordinary differential equations, particularly the Duffing oscillator. Analytical solutions for these differential equations can be time consuming whereas, conventional numerical solutions may lack accuracy. This research propose a block multistep method integrated with a variable order step size (VOS) algorithm for solving these Duffing oscillators directly. The proposed VOS Block method provides an alternative numerical solution by reducing computational cost (time) but without loss of accuracy. Numerical simulations are compared with known exact solutions for proof of accuracy and against current numerical methods for proof of efficiency (steps taken).