Macroeconomic Instability and Terrorism Nexus: Empirical Evidence in Case of Pakistan

The current study is an attempt to analyze the association between macroeconomic instability and terrorism in Pakistan over the period of 1970 to 2020. Six important variables are taken as a proxy to measure macroeconomic instability which includes external debt, budget deficit, trade deficit, real effective exchange rate (REER), inflation and unemployment. Results indicate that there exists a long run cointegration relationship between the indictors of macroeconomic instability and terrorism. FMOLS is employed to obtain the estimates and it reveals that budget deficit and external debt is negatively associated with terrorism. It indicates that government expenditures on different project such as infrastructure create economic opportunities, therefore, reduces terrorism. Furthermore, welfare programmes also improve the performance of socioeconomic variables that translates into harmonized environment which lessens violence. The variable of trade deficit, inflation and unemployment has positive impact on terrorism while REER is insignificant. In context of trade deficit, higher imports results in job loss of domestic industries, hence, it hits the vulnerable groups. Therefore, the opportunity cost of life of these groups reduces and it increases the probability to become a part of terrorist activities. Inflation also pushes the vulnerable groups in poverty by reduces the purchasing power and unemployed individuals are also easy target to get involve themselves in acts of aggression. This study also constructs the macroeconomic instability index including the six variables through principal component analysis (PCA). Results of this model show that macroeconomic instability index and GDP has positive effect on terrorism. In case of GDP, the plausible reason could be uneven income distribution that increases terrorist activities. For the policy implications, government need to divert the resources from non-productive to productive uses through the investment in such projects which has direct and indirect impact on the welfare. In this way deprived group will enjoy economic perks and engage themselves in productive activities rather than becoming a helping hand in terrorism.

Optimal Homotopy Asymptotic Method to Solution of Partial Differential Equations

Nonlinear Differential equations are of major importance in different fields of science and engineering. For complicated nonlinear problems exact solutions are not available and alternate way is to use numerical methods, Iterative methods or analytical techniques of perturbation. Numerical methods use discretization a have slow rate of convergence. Iterative methods are sensitive to initial conditions and in case of high nonlinearity they do not yield converged results. In perturbation methods small parameter is applied on the equation and hence cannot be applied for high nonlinear problems as they do not have small parameter. One of domain type methods is known as OHAM. This method is free from small parameter assumption and do not need the initial guess. The proposed method provides better accuracy at lower-order of approximations. Moreover the convergence domain can be easily adjusted. In this thesis OHAM is implemented for solution linear and nonlinear tenth order ODEs. Then its effectiveness and generalization is shown to a nonlinear family of PDEs, including Burger, Fisher, Burger’s–Huxley, Burger’s–Fisher, MEW and DGRLW equations. The results of the proposed method are compared with that of DTM, VIM, ADM, HAM and HPM, which reveal that OHAM is effective, simpler, easier and explicit. Apart from application to PDEs, OHAM is applied to couple system of PDEs. The coupled WBK, ALW, MB systems are used as test examples and results are compared with those obtained by HPM. OHAM is implemented to DDEs as well, and solution of MKdV lattice equation is presented for the illustration of proposed technique. The results are compared with HAM and HPM. In all cases the results obtained by OHAM are in close agreement with the exact solution and reveal high accuracy.