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Prof.  Srinivasarao  Thota
Amrita Vishwa Vidyapeetham,  India

Title: On A New Nonlinear Three-Step Root-Finding Algorithm for Transcendental Equations


The development of new numerical algorithms with higher convergence orders and lower computational costs is crucial in various scientific, engineering, and business applications. Nonlinear phenomena are ubiquitous in these fields, and accurate solutions often require efficient computational methods. In this context, the talk aims to introduce a novel three-step numerical algorithm designed to solve transcendental/nonlinear scalar and vector equations. In the proposed algorithm we use the third-order Halley’s algorithm as the starting step, aiming to increase the order of convergence and reduce the number of function evaluations in the exponential iterative algorithm.

The proposed numerical algorithm demonstrates ninth-order convergence. High-order convergence implies that the error decreases rapidly with each iteration, leading to faster and more accurate solutions. Despite its high convergence order, the scheme is computationally inexpensive. This feature is essential for practical applications, as it allows for the efficient solution of complex nonlinear problems without requiring excessive computational resources. The proposed algorithm requires only six function evaluations per iteration. Reducing the number of function evaluations contributes to computational efficiency and makes the method more feasible for real-world applications, especially when dealing with computationally expensive functions. In general, the development of a high-order, computationally inexpensive numerical scheme for solving nonlinear equations represents a significant advancement in computational science and holds promise for addressing challenging problems across various domains. Implementation of the proposed algorithm is presented in Maple with sample computations. 

Keyword: Root-finding algorithm; nonlinear equations; computational cost; Exponential method; Maple implementation. 


Prof. Srinivasarao Thota completed his M.Sc. in Mathematics from Indian Institute of Technology (IIT) Madras, India and Ph.D. in Mathematics from Motilal Nehru National institute of Technology (NIT) Allahabad, India. Thota’s areas of research interest are Computer Algebra (symbolic methods for differential equations), Numerical Analysis (root finding algorithms) and Mathematical Modelling (ecology). He has published more than 50 research papers in several international journals and presented his work in different national and international conferences as oral presenter and expertise/invited speaker. He is also editorial board member of various international journals and received several awards on academic/research work. Presently, he is working as Associate Professor at the Department of Mathematics, Amrita Vishwa Vidyapeetham, Amaravati, India. 

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