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Sunethra Weerakoon

Bio: Sunethra Weerakoon is an academic researcher from University of Sri Jayewardenepura. The author has contributed to research in topics: Firefly algorithm & Nonlinear system. The author has an hindex of 6, co-authored 13 publications receiving 905 citations. Previous affiliations of Sunethra Weerakoon include Pennsylvania State University & Curtin University.

Papers
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Journal ArticleDOI
TL;DR: It is shown that the order of convergence of the new method is three, and computed results support this theory.

813 citations

Journal ArticleDOI
TL;DR: In this paper, the Sumudu transform of partial derivatives is derived, and its applicability demonstrated using three different partial differential equations (PDEs) is demonstrated with respect to three different PDEs.
Abstract: The Sumudu transform of partial derivatives is derived, and its applicability demonstrated using three different partial differential equations.

114 citations

Journal ArticleDOI
TL;DR: This paper presents a modified firefly algorithm treating the problem as an optimization problem, which is capable of giving multiple root approximations simultaneously within a reasonable state space and illustrates the viability of the method using benchmark systems found in the literature.
Abstract: Most numerical methods that are being used to solve systems of nonlinear equations require the differentiability of the functions and acceptable initial guesses. However, some optimization techniques have overcome these problems, but they are unable to provide more than one root approximation simultaneously. In this paper, we present a modified firefly algorithm treating the problem as an optimization problem, which is capable of giving multiple root approximations simultaneously within a reasonable state space. The new method does not concern initial guesses, differentiability and even the continuity of the functions. Results obtained are encouraging, giving sufficient evidence that the algorithm works well. We further illustrate the viability of our method using benchmark systems found in the literature.

36 citations

Proceedings ArticleDOI
01 Jul 2016
TL;DR: A modified firefly algorithm with a self-tuning ability to solve a given univariate nonlinear equation within a reasonable interval/range and capable of tuning the algorithm-specific parameters while finding the optimum solutions is proposed.
Abstract: Existing numerical methods to solve univariate nonlinear equations sometimes fail to return the required results. We propose a modified firefly algorithm [MOD FA] with a self-tuning ability to solve a given univariate nonlinear equation. Our modification is capable of finding almost all real as well as complex roots of a nonlinear equation within a reasonable interval/range. The modification includes an archive to collect best fireflies and a flag to determine poorly performed iterations. It is also capable of tuning the algorithm-specific parameters while finding the optimum solutions. The self-tuning concept allows the users of our application to use it without any prior knowledge of the algorithm. We validate our approach on examples of some special univariate nonlinear equations with real as well as complex roots. We have also conducted a statistical test: the Wilcockson sign rank test. By conducting a comparison with the genetic algorithm and differential evolution with same modifications [MOD GA] [MOD DE] and with the original firefly algorithm [FA], we confirm the efficiency and the accuracy of our approach.

11 citations

Journal ArticleDOI
TL;DR: This paper extends the WFM to functions of several variables and provides a rigorous proof for the third order convergence and further analyse the method mathematically and demonstrates the reason for the strong performance of WFM computationally, despite it requiring more function evaluations.
Abstract: Weerakoon-Fernando Method (WFM) is a widely accepted third order iterative method introduced in the late 1990s to solve nonlinear equations. Even though it has become so popular among numerical analysts resulting in hundreds of similar work for single variable case, after nearly two decades, nobody took the challenge of extending the method to multivariable systems. In this paper, we extend the WFM to functions of several variables and provide a rigorous proof for the third order convergence. This theory was supported by computational results using several systems of nonlinear equations. Computational algorithms were implemented using MATLAB. We further analyse the method mathematically and demonstrate the reason for the strong performance of WFM computationally, despite it requiring more function evaluations.

10 citations


Cited by
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Journal ArticleDOI
TL;DR: A novel metaheuristic optimization algorithm, gradient-based optimizer (GBO) is proposed, which yielded very promising results due to its enhanced capabilities of exploration, exploitation, convergence, and effective avoidance of local optima.

379 citations

Journal ArticleDOI
TL;DR: The third or fifth order of convergence of these variants of Newton's method for dimension one, and the second or third order in several variables, depending on the behaviour of the second derivative are proved.

366 citations

Journal ArticleDOI
TL;DR: In this paper, the Sumudu transform is used to solve problems without resorting to a new frequency domain, which is the theoretical dual to the Laplace transform, and hence ought to rival it in problem solving.
Abstract: The Sumudu transform, whose fundamental properties are presented in this paper, is still not widely known, nor used. Having scale and unit-preserving properties, the Sumudu transform may be used to solve problems without resorting to a new frequency domain. In 2003, Belgacem et al. have shown it to be the theoretical dual to the Laplace transform, and hence ought to rival it in problem solving. Here, using the Laplace-Sumudu duality (LSD), we avail the reader with a complex formulation for the inverse Sumudu transform. Furthermore, we generalize all existing Sumudu differentiation, integration, and convolution theorems in the existing literature. We also generalize all existing Sumudu shifting theorems, and introduce new results and recurrence results, in this regard. Moreover, we use the Sumudu shift theorems to introduce a paradigm shift into the thinking of transform usage, with respect to solving differential equations, that may be unique to this transform due to its unit-preserving properties. Finally, we provide a large and more comprehensive list of Sumudu transforms of functions than is available in the literature.

299 citations

01 Jan 2003
TL;DR: A general error analysis providing the higher order of convergence is given, and the best efficiency, in term of function evaluations, of two of this new methods is provided.
Abstract: We present a new modification of the Newton's method which produces iterative methods with order of convergence three. A general error analysis providing the higher order of convergence is given, and the best efficiency, in term of function evaluations, of two of this new methods is provided.

264 citations

Journal ArticleDOI
TL;DR: In this article, a modification of the Newton's method is presented, which produces iterative methods with order of convergence three, and a general error analysis is given, and the best efficiency, in terms of function evaluations, of two of these methods is provided.

245 citations