Browsing by Author "Kajanthan, S."

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A class of s-step non-linear iteration scheme based on projection method for s-stage Runge-Kutta method.
(International Research Symposium on Pure and Applied Sciences, 2017 Faculty of Science, University of Kelaniya, Sri Lanka., 2017) Kajanthan, S.; Vigneswaran, R.
A variety of linear iteration schemes with reduced linear algebra costs have been proposed to solve the non-linear equations arising in the implementation of implicit Runge-Kutta methods as an alternative to the modified Newton iteration scheme. In this paper, a class of s-step non-linear scheme based on projection method is proposed to accelerate the convergence rate of those linear iteration schemes. The s-step scheme is given. where is a scalar, O the zero vector. In this scheme, sequence of numerical solutions is updated after each sub-step is completed. The efficiency of this scheme was examined when it is applied to the linear scalar problem with rapid convergence required for all in the left half complex plane, where is a step size, and obtained the iteration matrix of this scheme. The non-singular matrix Q should be chosen to minimize the maximum of the spectral radius of the iteration matrix over the left half complex plane. For 2-stage Gauss method, upper bound for the spectral radius of the iteration matrix was obtained in the left half complex plane. In this approach, it is difficult to handle the 3-stage Gauss method and 4-stage Gauss methods. We transform the coefficient matrix and the iteration matrix to a block diagonal matrix. The result for s=2 is applied to other methods when s>2. Finally, some numerical experiments are carried out to confirm the obtained theoretical results. Numerical result shows that, the proposed class of non- linear iteration scheme accelerates the convergence rate of the linear iteration scheme that we consider for the comparison in this work. It will be possible to apply the proposed class of non-linear scheme to accelerate the rate of convergence of other linear iteration schemes.
Forecasting the chilli production in Kurunegala district
(Faculty of Science, University of Kelaniya, Sri Lanka, 2021) Kajanthan, S.; Selvarajah, P.; Mufliha, A.W.F.
In Sri Lanka about 27.1% of its working population is engaged in agriculture, which occupies about 7.54 % of the Gross Domestic Production (GDP). Chilli plays a major role in sustainable agriculture production. However, due to climatic changes, the pattern of chilli production has changed drastically during the past few decades in the Kurunegala district and has severely affected agricultural production. Therefore, this study aims to detect the pattern of the production and forecast and predict the factors impacting on the production during both Yala and Maha seasons from 2001 to 2019. Yearly production of Chilli had been decreasing during Yala and Maha seasons. But, there had been a big change in the production during the Yala season from 2014 to 2017. And also there was a change in the Chilli production level during Maha season from 2013 to 2019. Due to the volatility in the yearly production, a best time series model is selected for forecasting the Chilli production. It was founded that, a best time series model ARIMA (0, 1, 1) fitted for forecasting the Chilli production during the Yala season and ARIMA (0, 1, 2) model fitted for forecasting the chilli production during the Maha season. Moreover, the adequacy of the fitted best model has been tested using Ljung-Box test and Correlation matrix test. Both seasons, the long-term future forecast production values have increased. Another study was carried out to find out the significant factors affecting the productivity of the chilli in both the Yala and Maha seasons. Temperature, rainfall, relative humidity and cloud cover are the significant factors of affecting chilli production. The multiple linear regression analysis shows that temperature, relative humidity and cloud cover have been the significant factors of the chilli production during the Yala Season and the rainfall has been a significant factor of chilli production during Maha season. Kurunegala is categorised under an intermediate zone, therefore all climatic parameters affect a medium level and they help to achieve maximum production of crops that are cultivated in this district.
Valuation of American put option with transaction cost and dividend using logarithmic front fixing transformation
(Faculty of Science, University of Kelaniya Sri Lanka, 2024) Kajanthan, S.; Selvarajah, P.
Due to their early exercise features, American-style options are the most traded in the financial markets. Black-Scholes derive the well-known option pricing Partial Differential Equation (PDE) with some assumptions. Black-Scholes assumes no transaction costs in his option pricing PDE. However, considering transaction costs makes the holder's and writer's option prices not unique, indicating the real-world complexities of trading. This study illustrates the understanding of how transaction costs impact American option pricing. The American-style option pricing problem is a moving boundary problem due to the early exercise feature. The front-fixing transformation technique can be employed to convert a moving boundary problem into a fixed boundary problem. In this work, we used a discrete hedging strategy to derive the option pricing PDEs to evaluate the holder's and writer's option prices and then apply the Logarithmic Front Fixing Transformation (Landau Transformation) to transform them into fixed boundary PDE systems. Then the explicit finite difference scheme is used to obtain numerical solutions. Numerical results confirm that the holder's and writer's option prices are not unique due to the inclusion of the transaction cost. Holders will choose to buy an option at a lower price, in contrast, writers will choose to sell an option at a higher price. The optimal exercise price of the American put option price is higher with transaction costs suggesting that option holders may exercise early to minimize losses, adding practical insight into trading strategies. Additionally, the faster execution time due to the front-fixing technique contributes to more efficient numerical methods in financial modeling.