Novriana Sumarti

A highly stable deferred correction scheme with interpolant for systems of nonlinear two-point boundary value problems

Iterated deferred correction is a very popular approach to the numerical solution of general first-order systems of nonlinear two-point boundary value problems. Typically the order of accuracy of the solution is increased by 2 each time that a deferred correction is applied and this allows inexpensive local error estimates to be computed using embedding. Recent research has shown how deferred correction schemes having the very desirable property of superconvergence can be derived. This marks a significant step forward in the design of deferred correction algorithms although the price to be paid for superconvergence is that it is difficult to derive realistic embedded local error estimates. In the present paper we show that Richardson extrapolation is a viable alternative for error estimation and we consider in some detail the relative merits of embedding and extrapolation. Guided by this analysis we are able to derive for the first time a Lobatto deferred correction code which is very efficient for the solution of stiff problems, particularly in cases where the MIRK code TWPBVP.f is unstable. Furthermore we are able to derive efficient interpolants for this Lobatto code which are also applicable to MIRK formulae and we consider the problem of estimating the error in these interpolants. This completely solves the interpolation problem for our deferred correction codes apart perhaps for deriving interpolants for extremely stiff problems. This new Lobatto code is available on the web page of one of the present authors and fills a large gap in currently available deferred correction software.

Implementation of the dynamical system of the deposit and loan growth based on the Lotka-Volterra model and the improved model

The Lotka-Volterra model is a very popular mathematical model based on the relationship in Ecology between predator, which is an organism that eats another organism, and prey, which is the organism which the predator eats. Predator and prey evolve together. The prey is part of the predator’s environment, and the existence of the predator depends on the existence of the prey. As a dynamical system, this model could generate limit cycles, which is an interesting type of equilibrium sometime in the system of two or more dimensions. In [1,2], the dynamical system of the the Deposit and Loan Volumes based on the Lotka-Volterra Model had been developed. In this paper, we improve the definition of parameters in the model and then implement the model on the data of banking from January 2003 to December 2014 which consist of 4 (four) types of banks. The data is represented into the form of return in order to have data in a periodical-like form. The results show the periodicity in the deposit and loan growth data which is in line with paper in [3] that suggest the positive correlation between loan growth and deposit growth, and vice-versa.

Implementation of power barrier option valuation

Options are financial instruments that can be utilized to reduce risk in stock investment. Barrier options are one of the major types of options actively used in financial markets where its life period depends on the path of the underlying stock prices. The features of the barrier option can be used to modify other types of options. In this research, the barrier option will be implemented into power option, so it is called power barrier option. This option is an extension of the vanilla barrier options where the Call payoff being considered is defined as PC=max(STβ−Kβ,0), and the Put payoff being considered is defined as PP=max(Kβ−STβ,0). Here β > 0 and β ≠ 1, K is the strike price of the option, and ST is the price of the underlying stock at time maturity T. In this paper, we generate the prices of stock using binomial method which is adjusted to the power option. In the conclusion, the price of American power barrier option is more expensive than the price of European power barrier option.

A dynamical model on deposit and loan of banking: A bifurcation analysis

A dynamical model, which is one of sophisticated techniques using mathematical equations, can determine the observed state, for example bank profits, for all future times based on the current state. It will also show small changes in the state of the system create either small or big changes in the future depending on the model. In this research we develop a dynamical system of the form: dDdt=f(D,L,rD,rL,r),dLdt=g(D,L,rD,rL,r), Here D and rD are the volume of deposit and its rate, L and rL are the volume of loan and its rate, and r is the interbank market rate. There are parameters required in this model which give connections between two variables or between two derivative functions. In this paper we simulate the model for several parameters values. We do bifurcation analysis on the dynamics of the system in order to identify the appropriate parameters that control the stability behaviour of the system. The result shows that the system will have a limit cycle for small value of interest rate of loan, so ...

Stock and option portfolio using fuzzy logic approach

Fuzzy Logic in decision-making process has been widely implemented in various problems in industries. It is the theory of imprecision and uncertainty that was not based on probability theory. Fuzzy Logic adds values of degree between absolute true and absolute false. It starts with and builds on a set of human language rules supplied by the user. The fuzzy systems convert these rules to their mathematical equivalents. This could simplify the job of the system designer and the computer, and results in much more accurate representations of the way systems behave in the real world. In this paper we examine the decision making process of stock and option trading by the usage of MACD (Moving Average Convergence Divergence) technical analysis and Option Pricing with Fuzzy Logic approach. MACD technical analysis is for the prediction of the trends of underlying stock prices, such as bearish (going downward), bullish (going upward), and sideways. By using Fuzzy C-Means technique and Mamdani Fuzzy Inference System, we define the decision output where the value of MACD is high then decision is “Strong Sell”, and the value of MACD is Low then the decision is “Strong Buy”. We also implement the fuzzification of the Black-Scholes option-pricing formula. The stock and options methods are implemented on a portfolio of one stock and its options. Even though the values of input data, such as interest rates, stock price and its volatility, cannot be obtain accurately, these fuzzy methods can give a belief degree of the calculated the Black-Scholes formula so we can make the decision on option trading. The results show the good capability of the methods in the prediction of stock price trends. The performance of the simulated portfolio for a particular period of time also shows good return.

A mathematical model of interaction among humans, vampires and werewolves populations

In every country there are many fictional creatures depicting evil. In the western world, fictional creatures who often appear in horror stories are vampires and werewolves. Many released movies expose the conflict between humans with one or both creatures. In this paper, the interaction among humans, vampires and werewolves is modeled using a system of differential equations. We consider the stability of equilibrium points of the system that represent four situations; only humans remain or a disease-free condition, either vampires or werewolves are going to extinction, and no population goes extinct. The derived model is implemented for depicting some scenarios in the movie series of Underworld. The model can describe the fluctuation of vampires and werewolves population from the beginning to their extinction at 1500 years since the story started.In every country there are many fictional creatures depicting evil. In the western world, fictional creatures who often appear in horror stories are vampires and werewolves. Many released movies expose the conflict between humans with one or both creatures. In this paper, the interaction among humans, vampires and werewolves is modeled using a system of differential equations. We consider the stability of equilibrium points of the system that represent four situations; only humans remain or a disease-free condition, either vampires or werewolves are going to extinction, and no population goes extinct. The derived model is implemented for depicting some scenarios in the movie series of Underworld. The model can describe the fluctuation of vampires and werewolves population from the beginning to their extinction at 1500 years since the story started.

A modelling on estimation of the carbon dioxide emission from vehicles using logistic equation

In this paper, the logistic differential equation is used in developing a model on carbon dioxide traces which potentially releases from a particular area. The improvement to a higher scale or scope is straightforward by considering the larger observed data or larger number of the potential CO2 sources. Let G(t) the total amount of the carbon dioxide emission from motorcycles and cars used by the resident of the area. G(t)=P(t)(r1(t)η(t)+r2(t)ξ(t)) where P(t) is the number of the resident of the observed area (population of Bandung Institute of Technology) at year t, r1(t) and r2(t) are the portion of the population who use motorcycles and cars respectively, η(t) and ξ(t) are the approximated total emission of the carbon dioxide from the related vehicles respectively. The number of resident is modeled by the logistic equation so the future number can be estimated. The model is implemented in a campus of Institut Teknologi Bandung (ITB) at Ganesha street, Indonesia.The results show that the amount of CO2 p...

Modelling on corrosion inhibitor kinetics in carbon steel pipe used in oil industry

A model to explain the kinetics of corrosion inhibitor is proposed here. The model is based on Transition State Theory. Our model has many similarities with Michelis-Menten Kinetics. The kinetics difference between uninhibited corrosion and inhibited corrosion is presented. Our model showed the inhibitor could suppress the corrosion rate.