Vijay Kumar Kukreja
@sliet.ac.in
Professor, Department of Mathematics
Sant Longowal Institute of Engineering & Technology, Longowal
RESEARCH, TEACHING, or OTHER INTERESTS
Mathematics, Computational Mathematics, Numerical Analysis, Modeling and Simulation
59
Scopus Publications
806
Scholar Citations
16
Scholar h-index
24
Scholar i10-index
Scopus Publications
- A SIXTH-ORDER HERMITE COLLOCATION TECHNIQUE for NUMERICAL STUDY of NONLINEAR FISHER and BURGERS-FISHER EQUATIONS
ARCHNA KUMARI and VIJAY KUMAR KUKREJA
Cambridge University Press (CUP)
Abstract This study aims to formulate a highly accurate numerical method, specifically a seventh-order Hermite technique with an error term of sixth order, to solve the Fisher and Burgers–Fisher equations. This technique employs a combination of orthogonal collocation on the finite element method and hepta Hermite basis functions. By ensuring continuity of the dependent variable and its first three derivatives across the entire solution domain, it achieves a remarkable level of accuracy and smoothness. The space discretization is handled through the application of hepta Hermite polynomials, while the time discretization is managed by the Crank–Nicholson scheme. The stability and convergence analysis of the scheme are discussed in detail. To validate the accuracy of the proposed technique, three examples are taken. The results obtained from these examples are thoroughly analysed and compared against the exact solutions and reliable data from the existing literature. It is established that the proposed technique is easy to implement and gives better results as compared with existing ones. - Numerical solution and analysis of extended Fisher–Kolmogorov equation using an improved collocation algorithm
Shallu and V. K. Kukreja
Informa UK Limited - New Hermite collocation approach with shocks wave capturing for solving non-linear coupled Burgers-type model at high Reynolds number
Archna Kumari, Sudhir Kumar, and Vijay Kumar Kukreja
Springer Science and Business Media LLC - Study of generalized regularized long wave equation via septic Hermite collocation method with Crank–Nicolson and SSP-RK43 schemes to capture the various solitons
Archna Kumari and Vijay Kumar Kukreja
Elsevier BV - Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations
Archna Kumari and Vijay K. Kukreja
With progress on both the theoretical and the computational fronts, the use of Hermite interpolation for mathematical modeling has become an established tool in applied science. This article aims to provide an overview of the most widely used Hermite interpolating polynomials and their implementation in various algorithms to solve different types of differential equations, which have important applications in different areas of science and engineering. The Hermite interpolating polynomials, their generalization, properties, and applications are provided in this article. - Study of 4<sup>th</sup> order Kuramoto-Sivashinsky equation by septic Hermite collocation method
Archna Kumari and Vijay Kumar Kukreja
Elsevier BV - Solution of the generalized regularized long-wave equation with optimal spline collocation technique and implicit Crank–Nicolson as well as explicit SSP-RK43 scheme
Shallu and V. K. Kukreja
Informa UK Limited
In this work, a generalized regularized long-wave equation is solved using the optimal cubic B-spline collocation method for space discretization. Two different approaches are followed for the time-domain discretization. One is the implicit Crank–Nicolson scheme and the other is strong explicit stability preserving Runge–Kutta method of four stages and third-order. Also, the stability analysis of the techniques is carried out and it is shown that the implicit technique is unconditional stable, whereas the explicit technique is conditionally stable. These methods are applied to three problems involving a single solitary wave, the interaction of two solitary waves, and the evolution of solitons via the Maxwellian initial condition. These equations possess three invariants of motion that are mass, momentum, and energy. The value of these invariants is calculated, which is found to remain preserved for a long time. To demonstrate the robustness of both the techniques, the and error norms are calculated. - Shishkin mesh based septic Hermite interpolation algorithm for time-dependent singularly perturbed convection–diffusion models
Archna Kumari and V. K. Kukreja
Springer Science and Business Media LLC - Solution of Dual Boundary Layer Singular Perturbation Problem by Septic Hermite Collocation Technique
Archna Kumari, Shallu, and V. K. Kukreja
Springer Science and Business Media LLC - An improvised collocation algorithm to solve generalized Burgers’–Huxley equation
Shallu and Vijay Kumar Kukreja
Springer Science and Business Media LLC
AbstractIn the proposed work, an improvised collocation technique with cubic B-spline as basis functions is applied to obtain the numerical solution of non-linear generalized Burgers’–Huxley equation, which has application in the soliton theory. In this technique, posteriori corrections are made to the cubic B-spline interpolant and its higher-order derivatives, which leads to enhancement in the order of convergence in the spatial domain. The temporal domain is discretized using a weighted finite difference scheme, to obtain the solution at each time level and the spatial domain is discretized using the improvised cubic B-spline collocation method. The stability analysis is carried out using the von Neumann scheme and the technique is found to be unconditionally stable. The theoretical proof of the order of convergence is discussed in detail using Green’s function approach. The $$L_{2}$$ L 2 , $$L_{\\infty }$$ L ∞ , and absolute error norms are calculated as well as compared with the results available in the literature, which shows the improvement and efficacy of the proposed technique over the existing ones. - Numerical treatment of Benjamin-Bona-Mahony-Burgers equation with fourth-order improvised B-spline collocation method
Shallu and V.K. Kukreja
Elsevier BV - Error bounds for septic Hermite interpolation and its implementation to study modified Burgers’ equation
Archna Kumari and V. K. Kukreja
Springer Science and Business Media LLC - Computational analysis of some partial differential equations using efficient compact finite difference method
Ravneet Kaur and V. K. Kukreja
AIP Publishing - An improvised extrapolated collocation algorithm for solving Kuramoto–Sivashinsky equation
Shallu and Vijay Kumar Kukreja
Wiley
In the present work, the numerical solution of the Kuramoto–Sivashinsky (KS) equation is obtained using an improvised quintic B‐spline extrapolated collocation technique. This equation helps in the study of wave production in dissipative medium, investigates the hydrodynamic uncertainty in laminar flames, describes the turbulence of diverse physical processes, and so on. In this work, splines are used due to their higher smoothness property and the sparse nature of the matrices corresponding to the B‐splines. The improvised B‐splines are formed by forcing the quintic B‐spline interpolant to satisfy the interpolatory and some special end conditions. These basis functions are used in the collocation method for space integration and a weighted finite difference scheme is used for temporal domain integration. The stability of the technique is analyzed using the von Neumann scheme, and it is found to be unconditionally stable. The proposed method is found to be sixth‐order convergent in space and second‐order convergent in the time direction. The theoretical order of convergence is matching perfectly with the numerical one. The efficiency of this scheme is demonstrated by applying it to a number of examples. The L2, L∞, and global relative errors are calculated and compared with the previous work, especially with those where quintic B‐splines are used as basis functions. Also, the behavior of some KS equations is discussed for which the exact solution is not available. The aim of the paper is to show that such an improvised technique can be implemented to solve partial differential equations like the KS equation. - Study of Self-Adjoint Singularly Perturbed BVP by Septic Hermite Collocation Method
Archna Kumari, Shallu Shallu, and V. K. Kukreja
Springer International Publishing - Sixth order Hermite collocation method for analysis of MRLW equation
Archna Kumari and Vijay Kumar Kukreja
Elsevier BV - A robust Hermite spline collocation technique to study generalized Burgers-Huxley equation, generalized Burgers-Fisher equation and Modified Burgers’ equation
Shelly Arora, Rajiv Jain, and V.K. Kukreja
Elsevier BV - Two different temporal domain integration schemes combined with compact finite difference method to solve modified Burgers’ equation
Ravneet Kaur, Shallu, V.K. Kukreja, Nabendra Parumasur, and Pravin Singh
Elsevier BV - Robust septic Hermite collocation technique for singularly perturbed generalized Hodgkin–Huxley equation
Archna Kumari and V.K. Kukreja
Informa UK Limited
In this paper, the singularly perturbed generalized Hodgkin–Huxley equation is solved by the septic Hermite collocation method (SHCM). In this method, septic Hermite interpolating polynomials are used to approximate the trial function because of their special properties such as continuity of the function and the continuity of its tangent at the grid points. The Crank–Nicolson scheme is applied for time discretization and the septic Hermite interpolating polynomials are used for space discretization. The Von-Neumann stability analysis is applied and the algorithm is found to be unconditionally stable. The efficiency of the numerical technique is demonstrated by solving some test examples and comparing the output with the literature data. The analysis shows that the present scheme is easy to implement and gives better results in contrast to the earlier ones. - Analysis of RLW and MRLW equation using an improvised collocation technique with SSP-RK43 scheme
Shallu and V.K. Kukreja
Elsevier BV - Analysis of a linear and non-linear model for diffusion–dispersion phenomena of pulp washing by using quintic Hermite interpolation polynomials
Satinder Pal Kaur, Ajay Kumar Mittal, V. K. Kukreja, Archna Kaundal, N. Parumasur, and P. Singh
Springer Science and Business Media LLC - An Efficient Collocation Algorithm with SSP-RK43 Scheme to Solve Rosenau–KdV–RLW Equation
Shallu and Vijay Kumar Kukreja
Springer Science and Business Media LLC - An Improved Extrapolated Collocation Technique for Singularly Perturbed Problems using Cubic B-Spline Functions
Shallu, Archna Kumari, and Vijay Kumar Kukreja
Springer Science and Business Media LLC
RECENT SCHOLAR PUBLICATIONS
- Numerical solution and analysis of extended Fisher–Kolmogorov equation using an improved collocation algorithm
Shallu, VK Kukreja
International Journal of Computer Mathematics 102 (3), 415-434 2025 - Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem
VK Kukreja
Computational Methods for Differential Equations 13 (2), 578-591 2025 - A SIXTH-ORDER HERMITE COLLOCATION TECHNIQUE FOR NUMERICAL STUDY OF NONLINEAR FISHER AND BURGERS–FISHER EQUATIONS
A KUMARI, VK KUKREJA
The ANZIAM Journal 67, e12 2025 - New Hermite collocation approach with shocks wave capturing for solving non-linear coupled Burgers-type model at high Reynolds number
A Kumari, S Kumar, VK Kukreja
Engineering with Computers, 1-16 2024 - Highly accurate collocation methodology for solving the generalized Burgers-Fisher’s equation
S Shallu, VK Kukreja
Iranian Journal of Numerical Analysis and Optimization 14 (3), 736-761 2024 - Study of generalized regularized long wave equation via septic Hermite collocation method with Crank–Nicolson and SSP-RK43 schemes to capture the various solitons
A Kumari, VK Kukreja
Wave Motion 122, 103188 2023 - Survey of Hermite interpolating polynomials for the solution of differential equations
A Kumari, VK Kukreja
Mathematics 11 (14), 3157 2023 - Study of 4th order Kuramoto-Sivashinsky equation by septic Hermite collocation method
A Kumari, VK Kukreja
Applied Numerical Mathematics 188, 88-105 2023 - Solution of the generalized regularized long-wave equation with optimal spline collocation technique and implicit Crank–Nicolson as well as explicit SSP-RK43 scheme
Shallu, VK Kukreja
International Journal of Computer Mathematics 100 (1), 1-19 2023 - Solution of Two-Point Boundary Value Problems Using Quintic Hermite Collocation Method
SP Kaur, AK Mittal, VK Kukreja
MRSPTU, Bathinda 2023 - Shishkin mesh based septic Hermite interpolation algorithm for time-dependent singularly perturbed convection–diffusion models
A Kumari, VK Kukreja
Journal of Mathematical Chemistry 60 (10), 2029-2053 2022 - Solution of dual boundary layer singular perturbation problem by septic Hermite collocation technique
A Kumari, Shallu, VK Kukreja
International Journal of Applied and Computational Mathematics 8 (5), 226 2022 - An optimal B-spline collocation technique for numerical simulation of viscous coupled Burgers’ equation
VK Kukreja
Computational Methods for Differential Equations 10 (4), 1027-1045 2022 - An improvised collocation algorithm to solve generalized Burgers'–Huxley equation.
VK Kukreja
Arabian Journal of Mathematics 11 (2) 2022 - An improvised collocation algorithm to solve generalized Burgers’–Huxley equation
Shallu, VK Kukreja
Arabian Journal of Mathematics 11 (2), 379-396 2022 - Sixth order Hermite collocation method for analysis of MRLW equation
A Kumari, VK Kukreja
Journal of Ocean Engineering and Science 2022 - A robust Hermite spline collocation technique to study generalized Burgers-Huxley equation, generalized Burgers-Fisher equation and Modified Burgers’ equation
S Arora, R Jain, VK Kukreja
Journal of Ocean Engineering and Science 2022 - Robust septic Hermite collocation technique for singularly perturbed generalized Hodgkin–Huxley equation
A Kumari, VK Kukreja
International Journal of Computer Mathematics 99 (5), 909-923 2022 - Error bounds for septic Hermite interpolation and its implementation to study modified Burgers’ equation
A Kumari, VK Kukreja
Numerical Algorithms 89 (4), 1799-1821 2022 - Numerical treatment of Benjamin-Bona-Mahony-Burgers equation with fourth-order improvised B-spline collocation method
VK Kukreja
Journal of Ocean Engineering and Science 7 (2), 99-111 2022
MOST CITED SCHOLAR PUBLICATIONS
- On a class of quadratically convergent iteration formulae
V Kanwar, VK Kukreja, S Singh
Applied mathematics and Computation 166 (3), 633-637 2005
Citations: 69 - Solution of two point boundary value problems using orthogonal collocation on finite elements
S Arora, SS Dhaliwal, VK Kukreja
Applied Mathematics and Computation 171 (1), 358-370 2005
Citations: 58 - On some third-order iterative methods for solving nonlinear equations
V Kanwar, VK Kukreja, S Singh
Applied Mathematics and Computation 171 (1), 272-280 2005
Citations: 58 - Numerical solution of Burgers’ equation by cubic Hermite collocation method
IA Ganaie, VK Kukreja
Applied Mathematics and Computation 237, 571-581 2014
Citations: 49 - Solution of Benjamin-Bona-Mahony-Burgers equation using collocation method with quintic Hermite splines
S Arora, R Jain, VK Kukreja
Applied Numerical Mathematics 154, 1-16 2020
Citations: 46 - Characterisation of honey produced from different fruit plants of northern India
V Nanda, B Singh, VK Kukreja, AS Bawa
International Journal of Food Science and Technology 44 (12), 2629-2636 2009
Citations: 44 - Simulation of washing of packed bed of porous particles by orthogonal collocation on finite elements
S Arora, SS Dhaliwal, VK Kukreja
Computers & chemical engineering 30 (6-7), 1054-1060 2006
Citations: 42 - Application of orthogonal collocation on finite elements for solving non-linear boundary value problems
S Arora, SS Dhaliwal, VK Kukreja
Applied mathematics and computation 180 (2), 516-523 2006
Citations: 30 - Numerical treatment of Benjamin-Bona-Mahony-Burgers equation with fourth-order improvised B-spline collocation method
VK Kukreja
Journal of Ocean Engineering and Science 7 (2), 99-111 2022
Citations: 26 - Cubic Hermite collocation solution of Kuramoto–Sivashinsky equation
IA Ganaie, S Arora, VK Kukreja
International Journal of Computer Mathematics 93 (1), 223-235 2016
Citations: 21 - An improvised collocation algorithm with specific end conditions for solving modified Burgers equation
Shallu, VK Kukreja
Numerical Methods for Partial Differential Equations 37 (1), 874-896 2021
Citations: 20 - Error bounds for septic Hermite interpolation and its implementation to study modified Burgers’ equation
A Kumari, VK Kukreja
Numerical Algorithms 89 (4), 1799-1821 2022
Citations: 19 - Solution of diffusion–dispersion models using a computationally efficient technique of orthogonal collocation on finite elements with cubic Hermite as basis
AK Mittal, IA Ganaie, VK Kukreja, N Parumasur, P Singh
Computers & chemical engineering 58, 203-210 2013
Citations: 19 - Numerical approach for solving diffusion problems using cubic B-spline collocation method
B Gupta, VK Kukreja
Applied Mathematics and Computation 219 (4), 2087-2099 2012
Citations: 19 - Mathematical modeling of a rotary vacuum washer used for pulp washing: a case study of a lab scale washer
VK Kukreja, AK Ray
Cellulose Chemistry & Technology 43 (1), 25 2009
Citations: 19 - A computationally efficient technique for solving two point boundary value problems in porous media
S Arora, SS Dhaliwal, VK Kukreja
Applied mathematics and computation 183 (2), 1170-1180 2006
Citations: 18 - Modeling of washing of brown stock on rotary vacuum washer
VK Kukreja
University of Roorkee, Roorkee 1996
Citations: 15 - A Mathematical model for pulp washing in different zones of a rotary vacuum filter
VK Kukreja, AK Ray, VP Singh, NJ Rao
INDIAN CHEMICAL ENGINEER SECTION A JOURNAL OF INDIAN INSTITUTE OF CHEMICAL 1995
Citations: 15 - A robust Hermite spline collocation technique to study generalized Burgers-Huxley equation, generalized Burgers-Fisher equation and Modified Burgers’ equation
S Arora, R Jain, VK Kukreja
Journal of Ocean Engineering and Science 2022
Citations: 14 - Analysis of RLW and MRLW equation using an improvised collocation technique with SSP-RK43 scheme
VK Kukreja
Wave Motion 105, 102761 2021
Citations: 13