Journal Articles
Permanent URI for this collectionhttps://idr.nitk.ac.in/handle/123456789/19884
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Item Consistency and feasibility of Haar wavelet collocation method for a nonlinear optimal control problem with application(World Scientific and Engineering Academy and Society, 2023) Madankar, S.R.; Setia, A.; M, M.; Agarwal, R.P.Haar wavelet-based numerical algorithms have recently been developed for various mathematical problems, including optimal control problems. However, no numerical algorithm is complete without its theoretical analysis. In this paper, we have shown the consistency and feasibility of the Haar wavelet-based collocation method for solving nonlinear optimal control problems that have a single state and a single control variable with constraints. The accuracy of the method has been shown through some application problems. © 2023, World Scientific and Engineering Academy and Society. All rights reserved.Item Error analysis of Haar wavelet-based Galerkin numerical method with application to various nonlinear optimal control problems(Taylor and Francis Ltd., 2024) Madankar, S.R.; Setia, A.; M, M.; Vatsala, A.S.First, this paper defines a general nonlinear optimal control problem with state/control constraints and its approximation problem as the Haar wavelet Galerkin optimal control problem (HWGOCP). Then, a Haar wavelet-based Galerkin numerical method has been developed, which converts it to a nonlinear optimization problem. We theoretically prove that a Haar wavelet feasible solution of HWGOCP will exist. We also show that the approximate solutions of HWGOCP are consistent and converge to the optimal solution of the problem. A variety of application problems have been considered, which include optimal control of tumour growth using Chemotherapy drugs, optimal control of infection via the SIS model using treatment, the Brachistochrone problem in mechanics, optimal control of mold using a fungicide, optimal control of pH value of a chemical reaction to determine the quality of a product, etc. © 2024 Informa UK Limited, trading as Taylor & Francis Group.Item Enhancing the applicability of Chebyshev-like method(Academic Press Inc., 2024) George, S.; Bate, I.; M, M.; Godavarma, C.; Senapati, K.Ezquerro and Hernandez (2009) studied a modified Chebyshev's method to solve a nonlinear equation approximately in the Banach space setting where the convergence analysis utilizes Taylor series expansion and hence requires the existence of at least fourth-order Fréchet derivative of the involved operator. No error estimate on the error distance was given in their work. In this paper, we obtained the convergence order and error estimate of the error distance without Taylor series expansion. We have made assumptions only on the involved operator and its first and second Fréchet derivative. So, we extend the applicability of the modified Chebyshev's method. Further, we compare the modified Chebyshev method's efficiency index and dynamics with other similar methods. Numerical examples validate the theoretical results. © 2024 Elsevier Inc.Item On obtaining convergence order of a fourth and sixth order method of Hueso et al. without using Taylor series expansion(Elsevier B.V., 2024) M, M.; Godavarma, G.; George, S.; Bate, I.; Senapati, K.Hueso et al. (2015) studied the fourth and sixth order methods to approximate a solution of a nonlinear equation in Rn, where the convergence analysis needs the involved operator to be five times differentiable and seven times differentiable for fourth-order and sixth-order methods, respectively. Also, they found no error estimate for those methods, as the Taylor series expansion played a leading role in proving the convergence. In this paper, we extended the method in the Banach space settings and relaxed the higher order derivative of the involved operator so that the methods can be used in a bigger class of problems which were not covered by the analysis in Hueso et al. (2015). Also, we obtained an error estimate without Taylor series expansion. This error estimate helps to get the number of iterations to achieve a given accuracy. Moreover, new sixth-order method is introduced by small modification and numerical examples were discussed for all these methods to validate our theoretical results and to study the dynamics. © 2024 Elsevier B.V.Item Upcycling iron-rich industrial waste into a carbon-sequestering composite binder through optimized carbonation curing for structural applications(Taylor and Francis Ltd., 2025) M, M.; Palanisamy, T.Background: Steel production generates large quantities of mill scale, a by-product rich in iron oxides, with global generation estimated at 13.5 million tons annually. Simultaneously, Portland cement production, essential for concrete, contributes nearly 8% of global CO2 emissions, highlighting the urgent need for low-carbon alternatives. Iron carbonate (FeCO3), typically regarded as a corrosion product, offers an underexplored opportunity for deliberate synthesis in binders to achieve both structural performance and CO2 sequestration. Repurposing mill scale into carbon-sink binders thus provides a dual pathway for waste valorization and climate change mitigation, while advancing circular economy and industrial symbiosis principles. Methods: A composite binder was developed using mill scale, fly ash, metakaolin, and limestone, with oxalic acid employed as a chelating agent to promote iron dissolution and carbonate formation. Specimens were subjected to carbonation curing under controlled CO2 pressures (1.5–3 bar) and analyzed using XRD, TGA/DTG, FTIR, and FESEM to evaluate phase development, carbonate formation, and microstructural features. Results: An oxalic acid dosage of 4% resulted in a 133% increase in compressive strength compared to the control. Specimens cured at 3 bar CO2 achieved compressive strength exceeding 65 MPa within 7 days, whereas 1.5 bar curing required 9 days. TGA confirmed CO2 uptake of approximately 10–11% by binder mass, while microstructural analysis revealed the presence of stable siderite and calcite phases. Conclusions: The carbon-sink binder, composed of more than 75% industrial by-products, substantially reduces carbon emissions and energy demand compared to cement-based systems. It shows strong potential as a low-carbon alternative for precast concrete, masonry, and pavement applications. Future work should focus on long-term durability, large-scale implementation, and life cycle performance to support its adoption in sustainable construction and policy frameworks. © 2025 Informa UK Limited, trading as Taylor & Francis Group.Item Convergence of Chun’s method in Banach spaces under weaker assumptions(Springer Science and Business Media B.V., 2025) George, S.; M, M.; Godavarma, C.In this paper, we give a modified convergence analysis for the fourth-order method studied in Cordero et al. (J Math Chem 53(1):430–449, 2015). Our analysis provides the convergence order using the derivative of the involved operator up to order two only, whereas their study needs it to be five times differentiable. Apart from this, this paper obtains the convergence ball radius and the number of iterations to reach the solution with the desired accuracy. Further, we use the general Banach space settings to get these results, while their work is done only for the space. At the end of the paper, we discuss a few numerical examples and compare them with other existing fourth-order methods. © The Author(s), under exclusive licence to The Forum D’Analystes 2025.Item Jarratt-type methods and their convergence analysis without using Taylor expansion(Elsevier Inc., 2025) Bate, I.; Senapati, K.; George, S.; M, M.; Godavarma, C.In this paper, we study the local convergence analysis of the Jarratt-type iterative methods for solving non-linear equations in the Banach space setting without using the Taylor expansion. Convergence analysis using Taylor series required the operator to be differentiable at least p+1 times, where p is the order of convergence. In our convergence analysis, we do not use the Taylor expansion, so we require only assumptions on the derivatives of the involved operator of order up to three only. Thus, we extended the applicability of the methods under study. Further, we obtained a six-order Jarratt-type method by utilising the method studied by Hueso et al. in 2015. Numerical examples and dynamics of the methods are presented to illustrate the theoretical results. © 2024 Elsevier Inc.Item A procedure for increasing the convergence order of iterative methods from p to 5p for solving nonlinear system(Academic Press Inc., 2025) George, S.; M, M.; Gopal, M.; Godavarma, C.; Argyros, I.K.In this paper, we propose a procedure to obtain an iterative method that increases its convergence order from p to 5p for solving nonlinear systems. Our analysis is given in more general Banach space settings and uses assumptions on the derivative of the involved operator only up to order max?{k,2}. Here, k is the order of the highest derivative used in the convergence analysis of the iterative method with convergence order p. A particular case of our analysis includes an existing fifth-order method and improves its applicability to more problems than the problems covered by the method's analysis in earlier study. © 2024Item Unified convergence analysis of a class of iterative methods(Springer, 2025) M, M.; George, S.; Godavarma, G.In this paper, unified convergence analyses for a class of iterative methods of order three, five, and six are studied to solve the nonlinear systems in Banach space settings. Our analysis gives the number of iterations needed to achieve the given accuracy and the radius of the convergence ball precisely using weaker conditions on the involved operator. Various numerical examples have been taken to illustrate the proposed method, and the theoretical convergence has been validated via these examples. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.Item Enhancing the applicability of Jarratt-type fourth-order and sixth-order iterative methods(Springer Science and Business Media Deutschland GmbH, 2025) M, M.; Godavarma, G.; George, S.In this paper, we extended the applicability of the convergence analysis of the sixth-order iterative methods for solving nonlinear equations studied by Yaseen and Zafar (Arab J Math 11:585-599, 2022), whose analysis uses derivatives up to order seven. Also, we have done convergence analysis for the fourth-order method which can be obtained from their method by considering first two steps. Our analysis is applicable in more general Banach space settings and uses only the first three Frechet derivatives of the involved operator with Lipschitz-type conditions. Also, our analysis gives the computable radius of the convergence ball and the number of iterations to obtain the solution with a given accuracy. © The Author(s) 2025.