Faculty Publications
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Publications by NITK Faculty
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Item On the local convergence and comparison between two novel eighth convergence order schemes for solving nonlinear equations(Cambridge Scientific Publishers, 2021) Regmi, S.; Argyros, I.K.; George, S.; Argyros, C.I.We compare two eighth order schemes for solving nonlinear equations involving Banach space valued equations. This is done by using assumptions only on the first derivative that does appear on the schemes, whereas in earlier works up to the ninth derivative (not on the scheme) are used to establish the convergence. Our technique is so general that it can be used to extend the usage of other schemes along the same lines. © 2021. All Rights Reserved.Item On a novel seventh convergence order method for solving nonlinear equations and its extensions(World Scientific, 2022) Regmi, S.; Argyros, I.K.; George, S.; Argyros, C.We extend the applicability of a novel seventh-order method for solving nonlinear equations in the setting of Banach spaces. This is done by using assumptions only on the first derivative that does appear on the method, whereas in earlier works up to the eighth derivatives (not on the scheme) were used to establish the convergence. Our technique is so general that it can be used to extend the usage of other schemes along the same lines. © 2022 World Scientific Publishing Company.Item EXTENDING THE APPLICABILITY OF A SEVENTH-ORDER METHOD FOR EQUATIONS UNDER GENERALIZED CONDITIONS(Institute of Mathematics. Polish Academy of Sciences, 2023) Regmi, S.; Argyros, I.K.; George, S.; Argyros, C.I.We extend the applicability of a seventh-order method for solving Banach space-valued equations. This is achieved by using generalized conditions on the first derivative which only appears in the method. Earlier works use conditions up to the eighth derivative to establish convergence. Our technique is very general and can be used to extend the applicability of other methods along the same lines. © Instytut Matematyczny PAN, 2023.Item On the semilocal convergence analysis of a seventh order four step method for solving nonlinear equations(Ptolemy Scientific Research Press, 2024) Regmi, S.; Argyros, I.K.; George, S.; Argyros, C.I.We provide a semi-local convergence analysis of a seventh order four step method for solving nonlinear problems. Using majorizing sequences and under conditions on the first derivative, we provide sufficient convergence criteria, error bounds on the distances involved and uniqueness. Earlier convergence results have used the eighth derivative not on this method to show convergence. Hence, limiting its applicability. © 2024 by the authors; licensee PSRP, Lahore, Pakistan.