Sejarah dan Eksistensi Ekonomi Islam pada Era Global di Asia Tenggara

Sharia Economics of Southeast Asian countries has been existing, with a close relationship with their society, since the early arrival of Islam and its spreading in this archipelago through the period of the Islamic Kingdoms up till today. The unity of this Islamic economy with its society because the society has made their identity as Islam so that their habits, customs, economic system, and Worldview are identical to Islam. However, the implementation of the Islamic economic system and its financial activities were interrupted by the existing of colonialism. After their independence from colonization, the country such as Malaysia, Indonesia, and Brunei Darussalam initiated to raise awareness and conducted studies on the Islamic economic system. Even the government has a commitment to achieve the World's prominent center of Islamic economy. This year's report by The State of global Islamic economists reveal that ASEAN countries have succeeded in positioning their countries as a largest of sharia financial center in the world.

Improving Halley and Householder Methods Using Decomposition Techniques

In this thesis, two new methods for solution of nonlinear system of equations f(x) = 0 using two decomposition techniques are established, first is Adomian decomposition technique and second is Varsha decomposition technique. We expand f(x) to second order then apply both of these techniques one by one. The convergence order of both these algorithms is three and efficiency index is p 1/d =1.442. The main benefit of this scheme is that we get root of function even after one or two iterations, obviously has minimum computational complexity as compare to previous systems. Both methods almost give the same results and convergence orders. In practice, for large scale problems, many iterative methods can be derived by using two decomposition techniques with some modifications in Newton Raphson method. The order of convergence of new iteration formulas can be derived analytically and with the help of Maple. Some examples are given to illustrate the performance and precision of new algorithms. These algorithms can be assumed as generalization of old methods for solving nonlinear equations.