A Novel Numerical Scheme for a Class of Singularly Perturbed Differential-Difference Equations with a Fixed Large Delay E. Srinivas, K. Phaneendra Bulletin of the Karaganda University Mathematics Series, 2024 A trigonometric spline based computational technique is suggested for the numerical solution of layer behavior differential-difference equations with a fixed large delay. The continuity of the first order derivative of the trigonometric spline at the interior mesh point is used to develop the system of difference equations. With the help of singular perturbation theory, a fitting parameter is inserted into the difference scheme to minimize the error in the solution. The method is examined for convergence. We have also discussed the impact of shift or delay on the boundary layer. The maximum absolute errors in comparison to other approaches in the literature are tallied, and layer behavior is displayed in graphs, to demonstrate the feasibility of the suggested numerical method.
Security analysis of Three-Factor Authentication Protocol Based on Extended Chaotic-Maps Suresh Devanapalli, Kolloju Phaneendra 2022 Opju International Technology Conference on Emerging Technologies for Sustainable Development Otcon 2022, 2023 In data security network communication, the authentication protocol is crucial. Therefore, the authentication protocol must offer protection against all recognised threats, including password guessing, insider, and identity theft assaults. However, a lot of protocols in the literature fall short of these security standards. In this paper, we evaluate the very lately put out Shuming et al. protocl. The three-factor authentication protocol demonstrates that it is susceptible to assaults from privileged insiders, offline password guessing attacks, user identity attacks, and parallel session attacks; as a result, their system is unable to thwart known session-based transient data attacks. Additionally, it lacks robust user anonymity and is susceptible to DoS and smart card loss attacks.
COMPUTATIONAL SCHEME FOR A DIFFERENTIAL DIFFERENCE EQUATION WITH A LARGE DELAY IN CONVECTION TERM Srinivas Erla, Phaneendra Kolloju International Journal of Applied Mechanics and Engineering, 2023 A computational scheme for the solution of layer behaviour differential equation involving a large delay in the derivative term is devised using numerical integration. If the delay is greater than the perturbation parameter, the layer structure of the solution is no longer preserved, and the solution oscillates. A numerical method is devised with the support of a specific kind of mesh in order to reduce the error and regulate the layered structure of the solution with a fitting parameter. The scheme is discussed for convergence. The maximum errors in the solution are tabulated and compared to other methods in the literature to verify the accuracy of the numerical method. Using this specific kind of mesh with and without the fitting parameter, we also studied the layer and oscillatory behavior of the solution with a large delay.
Numerical solution of differential – difference equations having an interior layer using nonstandard finite differences R. Omkar, M. Lalu, K. Phaneendra Bulletin of the Karaganda University Mathematics Series, 2023 This paper addresses the solution of a differential-difference type equation having an interior layer behaviour. A difference scheme is suggested to solve this equation using a non-standard finite difference method. Finite differences are derived from the first and second order derivatives. Using these approximations, the given equation is discretized. The discretized equation is solved using the algorithm for the tridiagonal system. The method is examined for convergence. Numerical examples are illustrated to validate the method. Maximum errors in the solution, in contrast to the other methods are organized to justify the method. The layer behaviour in the solution of the examples is depicted in graphs.
FOURTH ORDER COMPUTATIONAL SPLINE METHOD FOR TWO-PARAMETER SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM Satyanarayana KAMBAMPATI, Siva Prasad EMINENI, Chenna Krishna REDDY M., Phaneendra KOLLOJU International Journal of Applied Mechanics and Engineering, 2023 The current research work considers a two-parameter singularly perturbed two-point boundary value problem. Here, we suggest a computational scheme derived by using an exponential spline for the numerical solution of the problem on a uniform mesh. The proposed numerical scheme is analyzed for convergence and an accuracy of O(h4) is achieved. Numerical experiments are considered to validate the efficiency of the spline method, and compared comparison with the existing method to prove the superiority of the proposed scheme.
Computational Approach to Solving a Layered Behaviour Differential Equation with Large Delay Using Quadrature Scheme Amala Pandi, Lalu Mudavath, Phaneendra Kolloju International Journal of Applied Mechanics and Engineering, 2022 This paper deals with the computational approach to solving the singularly perturbed differential equation with a large delay in the differentiated term using the two-point Gaussian quadrature. If the delay is bigger than the perturbed parameter, the layer behaviour of the solution is destroyed, and the solution becomes oscillatory. With the help of a special type mesh, a numerical scheme consisting of a fitting parameter is developed to minimize the error and to control the layer structure in the solution. The scheme is studied for convergence. Compared with other methods in the literature, the maximum defects in the approach are tabularized to validate the competency of the numerical approach. In the suggested technique, we additionally focused on the effect of a large delay on the layer structure or oscillatory behaviour of the solutions using a special form of mesh with and without a fitting parameter. The effect of the fitting parameter is demonstrated in graphs to show its impact on the layer of the solution.
A variable mesh finite difference scheme for two-parameters singularly perturbed boundary value problems Journal of Mathematical Control Science and Applications, 2020
Fourth-order method for singularly perturbed singular boundary value problems using non-polynomial spline Maejo International Journal of Science and Technology, 2018
Non standard fitted finite difference method for singular perturbation problems using cubic spline Global and Stochastic Analysis, 2017
Solution of two parameters singular perturbation problem using higher order compact numerical method Global and Stochastic Analysis, 2017
An exponentially fitted non symmetric finite difference method for singular perturbation problems Wseas Transactions on Mathematics, 2013
Numerical integration method for singular perturbation delay differential equations with layer or oscillatory behaviour Applied and Computational Mathematics, 2013
Numerical treatment of singularly perturbed singular two-point boundary value problem using non-polynomial Spline in optimal control problems International Review of Automatic Control, 2012
A computational scheme for 1D time-dependent singularly perturbed parabolic differential-difference equations ES Prasad, K Phaneendra Computational Mathematics and Mathematical Physics 65 (2), 236-251 , 2025 2025 Citations: 1
Computational approach for a two-parameter convection- diffusion problem using an adaptive spline K. Satyanarayana, E. Siva Prasad, M. Chenna Krishna Reddy, K. Phaneendra∗ Journal of the Indian Math. Soc. ISSN (Print): 0019–5839. 92 (1), 98-109 , 2025 2025
A novel numerical scheme for a class of singularly perturbed differential-difference equations with a fixed large delay E Srinivas, K Phaneendra Bulletin of the Karaganda University. Mathematics Series 113 (1), 194-207 , 2024 2024 Citations: 2
Computation Method for a Differential-Difference Equation with Boundary Layer in Neuronal Variability Modelling using a Mixed Nonpolynomial Spline KP K. Mamatha, BSL Soujanya G Tuijin Jishu/Journal of Propulsion Technology, Vol. 45 45 (4), 29-39 , 2024 2024
Numerical solution of differential–difference equations having an interior layer using nonstandard finite differences R Omkar, M Lalu, K Phaneendra Bulletin of the Karaganda university. Mathematics series 110 (2), 104-115 , 2023 2023 Citations: 3
A Trigonometric Spline Method for a Singularly Perturbed Parabolic Time-Dependent Partial Differential-Difference Equations Arising in Computational Neuroscience M Lalu, K Phaneendra 2023
Trigonometric spline method for boundary layer differential difference equations with mixed shifts K Phaneendra, SP Emineni 1ST INTERNATIONAL CONFERENCE ON ESSENCE OF MATHEMATICS AND ENGINEERING … , 2023 2023
Security analysis of Three-Factor Authentication Protocol Based on Extended Chaotic-Maps S Devanapalli, K Phaneendra 2022 OPJU International Technology Conference on Emerging Technologies for … , 2023 2023
CRYPTANALYSIS ON “PRACTICAL AND PROVABLY SECURE THREE-FACTOR AUTHENTICATION PROTOCOL BASED ON EXTENDED CHAOTIC-MAPS FOR MOBILE LIGHTWEIGHT DEVICES” S Devanapalli, K Phaneendra International Journal of Advances in Soft Computing and Intelligent Systems … , 2023 2023 Citations: 1
Numerical Simulation for a Differential Difference Equation With an Interior Layer P Amala, M Lalu, K Phaneendra Communications in Mathematics and Applications 14 (1), 187 , 2023 2023
Cryptanalysis on “An Improved RFID-based Authentication Protocol for Rail Transit” S Devanapalli, K Phaneendra International Conference on Innovations in Intelligent Computing and … , 2022 2022
Numerical simulation of singularly perturbed delay differential equations with large delay using an exponential spline R Omkar, K Phaneendra International Journal of Analysis and Applications 20, 63-63 , 2022 2022 Citations: 1
Provably secure pseudo-identity three-factor authentication protocol based on extended chaotic-maps for lightweight mobile devices D Suresh, V Odelu, AG Reddy, K Phaneendra, HS Kim IEEE Access 10, 109526-109536 , 2022 2022 Citations: 6
A numerical approach for singular perturbation problems with an interior layer using an adaptive spline E Srinivas, M Lalu, K Phaneendra Iranian Journal of Numerical Analysis and Optimization 12 (2), 355-370 , 2022 2022 Citations: 3
Research Article Fitted Parameter Exponential Spline Method for Singularly Perturbed Delay Differential Equations with a Large Delay ES Prasad, R Omkar, K Phaneendra 2022
Fitted parameter exponential spline method for singularly perturbed delay differential equations with a large delay ES Prasad, R Omkar, K Phaneendra Computational and Mathematical Methods 2022 (1), 9291834 , 2022 2022 Citations: 6
A numerical approach for singularly perturbed nonlinear delay differential equations using a trigonometric spline M Lalu, K Phaneendra Computational and Mathematical Methods 2022 (1), 8338661 , 2022 2022 Citations: 3
Solution of Singularly Perturbed Boundary Value Problems with Singularity Using Variable Mesh Finite Difference Method E Siva Prasad, K Phaneendra Journal of Dynamical Systems and Geometric Theories 19 (1), 113-124 , 2021 2021
Quadrature method with exponential fitting for delay differential equations having layer behavior M Lalu, K Phaneendra J. Math. Comput. Sci 25, 191-208 , 2021 2021 Citations: 3
Numerical approach for differential-difference equations having layer behaviour with small or large delay using non-polynomial spline ESP M Lalu, K. Phaneendra Soft Computing 25, 13709–13722 , 2021 2021 Citations: 8
MOST CITED SCHOLAR PUBLICATIONS
Provably secure pseudo-identity based device authentication for smart cities environment AG Reddy, D Suresh, K Phaneendra, JS Shin, V Odelu Sustainable cities and society 41, 878-885 , 2018 2018 Citations: 44
Mixed finite difference method for singularly perturbed differential difference equations with mixed shifts via domain decomposition L Sirisha, K Phaneendra, YN Reddy Ain Shams Engineering Journal 9 (4), 647-654 , 2018 2018 Citations: 37
Numerical Integration Method for Singularly Perturbed Delay Differential Equations GS 18. K. Phaneendra, Y.N. Reddy International Journal of Applied Science and Engineering 10 (3), 249-261 , 2012 2012 Citations: 36
Computational method for singularly perturbed delay differential equations with twin layers or oscillatory behaviour DK Swamy, K Phaneendra, AB Babu, YN Reddy Ain Shams Engineering Journal 6 (1), 391-398 , 2015 2015 Citations: 32
Accurate numerical method for singularly perturbed differential difference equations with mixed shifts DK Swamy, K Phaneendra, YN Reddy Khayyam J. Math 4 (2), 110-122 , 2018 2018 Citations: 27
A seventh order numerical method for singular perturbation problems PP Chakravarthy, K Phaneendra, YN Reddy Applied Mathematics and Computation 186 (1), 860-871 , 2007 2007 Citations: 21
Solution of Singularly Perturbed Differential‐Difference Equations with Mixed Shifts Using Galerkin Method with Exponential Fitting D Kumara Swamy, K Phaneendra, YN Reddy Chinese Journal of Mathematics 2016 (1), 1935853 , 2016 2016 Citations: 16
AFitted Numerov Method for Singular Perturbation Problems Exhibiting Twin Layers K Phaneendra, P Pramod Chakravarthy, YN Reddy Applied Mathematics and Information Sciences , 2010 2010 Citations: 15
Numerical solution of singularly perturbed delay differential equations using gaussion quadrature method K Phaneendra, M Lalu Journal of Physics: Conference Series 1344 (1), 012013 , 2019 2019 Citations: 13
20. Numerical Solution of Second Order Singularly Perturbed Differential– Difference Equations with Negative Shift YNR K. Phaneendra∗ , GBSL Soujanya International Journal of Nonlinear Science 18 (3), 200-209 , 2014 2014 Citations: 13
A fitted nonstandard finite difference method for singularly perturbed differential difference equations with mixed shifts DK Swamy, K Phaneendra, YN Reddy J. de Afrikana 3 (4), 1-20 , 2016 2016 Citations: 12
Gaussian quadrature for two-point singularly perturbed boundary value problems with exponential fitting K Phaneendra, M Lalu Communications in Mathematics and Applications, 447 , 2019 2019 Citations: 10
Non-Iterative Numerical Integration method for Singular Perturbation Problems exhibiting Internal and Twin Layers K Phaneendra, YN Reddy, G Soujanya International Journal of Applied Mathematics and Computation 3 (1), 9-20 , 2011 2011 Citations: 9
Numerical approach for differential-difference equations having layer behaviour with small or large delay using non-polynomial spline ESP M Lalu, K. Phaneendra Soft Computing 25, 13709–13722 , 2021 2021 Citations: 8
Numerical treatment of singular perturbation problems exhibiting dual boundary layers K Phaneendra, S Rakmaiah, MCK Reddy Ain Shams Engineering Journal 6 (3), 1121-1127 , 2015 2015 Citations: 8
Numerical Integration Method for Singularly Perturbed Delay Differential Equations K Phaneendra, G Soujanya, V Reddy Applied and Computational Mathematics , 2013 2013 Citations: 8
Numerical Integration of Singularly Perturbed Differential-Difference Problem Using Non Polynomial Interpolating Function. M Adilaxmi, D Bhargavi, K Phaneendra Journal of Informatics & Mathematical Sciences 11 (2) , 2019 2019 Citations: 7
Asymptotic - Numerical method for Third-Order Singular Perturbation Problems GS K. Phaneendra, Y.N. Reddy International Journal of Applied Science and Engineering 10 (3), 241-248 , 2012 2012 Citations: 7
Provably secure pseudo-identity three-factor authentication protocol based on extended chaotic-maps for lightweight mobile devices D Suresh, V Odelu, AG Reddy, K Phaneendra, HS Kim IEEE Access 10, 109526-109536 , 2022 2022 Citations: 6
Fitted parameter exponential spline method for singularly perturbed delay differential equations with a large delay ES Prasad, R Omkar, K Phaneendra Computational and Mathematical Methods 2022 (1), 9291834 , 2022 2022 Citations: 6