Numerical solution of PDE's by using Spline function in collocation and DQM.
64
Scopus Publications
559
Scholar Citations
12
Scholar h-index
13
Scholar i10-index
Scopus Publications
A New Uniform Hyperbolic Polynomial B-Spline Computational Scheme for 3rd-Order Pseudo-Parabolic Problem Mutum Zico Meetei, Mohammad Tamsir, Manoj Singh, Neeraj Dhiman, Faizan Ahmad Khan Mathematics, 2026 This work introduces a new UHPB-spline computation approach to approximate the pseudo-parabolic problem of order three, which exposes parabolic as well as hyperbolic physical appearance. The approach is used for the discretization of spatial derivatives, which contributes to better accuracy and flexibility. For the discretization of the time derivative, the FDM is employed, endorsing computational proficiency. The anticipated approach has significantly enhanced accuracy. Contrasting various existing approaches, the proposed process is tailored for handling the difficulty in the third-order problem while preserving accuracy and stability over extensive problems. A detailed von Neumann stability analysis confirms its unconditional stability, which makes it robust, especially for long-term simulations, while the numerical ROC demonstrates the second-order convergence both in space and in time. Two expressive examples are considered to determine the accuracy and usefulness of the projected process. Compared to existing techniques, the combination of UHPB-spline functions together with the Crank–Nicolson method and FDM is evidence of an influential and consistent tool to solve pseudo-parabolic problems of higher orders.
Numerical approximation of time-dependent 3D Burgers’ equations in the occurrence of high Reynolds numbers Mohammad Tamsir, Neeraj Dhiman Journal of Difference Equations and Applications, 2026 The purpose of this study gets up from the intrinsic challenges associated with high-dimensional nonlinear equations and the necessity for accurate and efficient numerical procedures for their approximations. This work presents a numerical investigation of the time-dependent 3D Burgers’ equations in the occurrence of very large Reynolds numbers. For this study, a differential quadrature method is coupled with third-order-modified B-spline functions. For this process, cubic hyperbolic B-spline (CHBS) and cubic trigonometric tension B-spline (CTTBS) functions are used as base functions. In this technique, the considered model equations are reduced to systems of ordinary differential equations that are solved by a Runge–Kutta method. It is established that the DQM, coupled with both choices of base functions, produces nearly equally accurate results for very high Reynolds numbers. In the case of low Reynolds number, the DQM coupled with CHBS base functions is the better choice.
Numerical approximation of the 3rd order pseudo-parabolic equation using collocation technique Neeraj Dhiman, Mohammad Tamsir, Khaled A. Aldwoah, Mohammed A. Almalahi, Waleed Adel Boundary Value Problems, 2024 This study presents a novel numerical approach for approximating the solution of third-order pseudo-parabolic partial differential equations (PDEs), which exhibit both parabolic and hyperbolic characteristics. The proposed method employs a cubic trigonometric tension B-spline collocation technique for spatial discretization, offering greater flexibility and accuracy compared to traditional spline methods. For time discretization, the finite difference method (FDM) is used, ensuring computational efficiency. Unlike many existing methods, our approach is tailored to handle the complexity of third-order equations while maintaining stability and accuracy over large-scale problems. The method’s unconditional stability is confirmed through a detailed von Neumann stability analysis, making it particularly robust for long-term simulations. Two illustrative examples are presented to demonstrate the method’s superior accuracy and flexibility in handling complex boundary conditions, as well as its ability to manage large-scale problems without requiring restrictive time steps. Compared to the existing methods, the combination of trigonometric tension B-splines with FDM proves to be a powerful and reliable tool for solving higher-order pseudo-parabolic equations.
Numerical Analysis of Dermal Cell-Sheet Wound Healing Model using B-spline collocation Scheme Neelam Rana, Neeraj Dhiman, Robin Singh 2024 15th International Conference on Computing Communication and Networking Technologies Icccnt 2024, 2024 In this study, we have explored a mathematical model (which is a partial differential equation type) for understanding the dynamical characteristics of extracellular matrix of dermal wound healing, which falls under the study of tissue engineering because during the healing process additional cell accumulate at that region forming a film of tissue. The biological process of wound healing depends on a number of factors, including contamination of the injured area, wound dimension, oxygenation of the tissues and the rapid growth of the cell count, making the dynamic of wound healing quite intricate to study even for any prediction hence, a mechanistic mathematical model has been considered for the study of cell regeneration. And for the same dermal cell interaction model a numerical approach has been initiated in this study by implementing cubic b-spline collocation scheme.
Redefine trigonometric cubic B-spline collocation scheme for solving convection-diffusion equation Ashish Kumar Rawat, Neeraj Dhiman, Anand Chauhan, Saumya Gupta International Journal of Computing Science and Mathematics, 2024 Redefining the formulation of the trigonometrical cubic B-spline, collocation-based scheme is used to approximate the numerical solution of the convection-diffusion partial differential equation (PDE). This proposed work is based on the usual discretisation of the linear and non-linear terms of the PDE. The Robin-Graves technique is used to linearise the non-linear terms of the PDE, whether initial values are recalled by the initial or boundary condition. The finite difference scheme applies to this work for discretised time variable terms of the convection-diffusion equation. To establish the scheme, an example is compared with existing results, and the comparison is finer than the existing result. In this paper, we propose a modern technique that has impressive results compared to the previous technique. In the future, malaria type convection equation will be simulated by a redefine trigonometric function with a collocation scheme to understand the increment phenomena of the malaria parasite.
Finite Element Analysis of Two Disk Rotor System used in Automobile Turbochargers Sono Bhardawaj, Abhishek Kumar Jha, Rakesh Chandmal Sharma, Srihari Palli, Dharmana Lokanadham, Neeraj Sharma, Neeraj Dhiman International Journal of Vehicle Structures and Systems, 2023 Turbochargers are the devices which increase efficiency of the driving engines. For power boosters in engine such type of device is using in present scenario. Due to the complex design of turbocharger, its analysis is very difficult. A lot of literature is present about turbochargers but the complete analysis by using finite element method is rarely found in past. In the present work, a two overhung-disk rotor mounted on a shaft is modelled as turbochargers for sake of simplicity. Moreover, finite element analysis method is used for the complete analysis of the system. The Campbell diagram and eigenvectors are plotted for different modes for vibration analysis of the proposed system. Along with this, amplitude and phase response are also plotted with respect to rotor spin speed.
Dynamic Behaviour of Railway Vehicle under Bump and Pothole Track Irregularities Rakesh Chandmal Sharma, Srihari Palli, Sono Bhardawaj, Abhishek Kumar Jha, Azad Duppala, Neeraj Sharma, Sameer Sharma, Neeraj Dhiman International Journal of Vehicle Structures and Systems, 2023 The railway vehicle moving on a track is subjected to several types of track irregularities. The random track irregularities are statistical and usually modelled as stationary and ergodic functions. The periodic track irregularities mainly are sinusoid, damped sinusoid, cusp, bump, jog, plateau, trough and pothole. These deterministic inputs i.e. sinusoid, damped sinusoid, cusp, bump is usually modelled through exponential or sine functions, whereas jog, plateau, trough are represented through an elliptical or parabolic mathematical function. In the present work, 27 degrees of freedom railway vehicle is modelled using Lagrangian method. Its vibrational response and ride behaviour are analysed under bump and pothole inputs. The ride evaluation is carried out using Sperling Ride Index.
Pressure corrections in the potential flow analysis of electrohydrodynamics Kelvin-Helmholtz instability of cylindrical interface through porous media Gazi University Journal of Science, 2015
Variants of R-weakly commuting mappings and common fixed point theorems in intuitionistic fuzzy metric spaces Kuwait Journal of Science, 2014
Study of photoluminescence behaviour of porous silicon samples prepared at 20mA current density Journal of Nano and Electronic Physics, 2013
Electrohydrodynamic Kelvin - Helmholtz instability of cylindrical interface through porous media International Journal of Fluid Mechanics Research, 2013
Linear three dimensional thermal stability of a viscous fluid in rotating cubical cavity Advances and Applications in Fluid Mechanics, 2012
RECENT SCHOLAR PUBLICATIONS
Numerical approximation of time-dependent 3D Burgers’ equations in the occurrence of high Reynolds numbers M Tamsir, N Dhiman Journal of Difference Equations and Applications 32 (3), 412-424 , 2026 2026
A new uniform hyperbolic polynomial B-spline computational scheme for 3rd-order pseudo-parabolic problem MZ Meetei, M Tamsir, M Singh, N Dhiman, FA Khan Mathematics 14 (3), 542 , 2026 2026 Citations: 1
Numerical characterization of brain tumor density using a hybrid B-spline collocation approach N Rana, N Dhiman, R Singh, W Adel International Journal of Dynamics and Control 13 (12), 422 , 2025 2025
A Collocation Approach Using Cubic Unified Extended Trigonometric Tension B-Splines for Solving the Time-Fractional Telegraph Equation M Tamsir, N Dhiman, D Nigam, A Chauhan, W Adel Computational Methods for Differential Equations , 2025 2025
Numerical approximation to predict neoadjuvant chemotherapy outcomes in cancer patients using trigonometric tension B-spline collocation N Rana, N Dhiman, R Singh, M Tamsir, W Adel Ricerche di Matematica, 1-27 , 2025 2025 Citations: 2
Numerical treatment of the sine-Gordon equations via a new DQM based on cubic unified and extended trigonometric B-spline functions M Tamsir, MZ Meetei, N Dhiman Wave Motion 131, 103409 , 2024 2024 Citations: 2
Numerical approximation of the 3rd order pseudo-parabolic equation using collocation technique N Dhiman, M Tamsir, KA Aldwoah, MA Almalahi, W Adel Boundary Value Problems 2024 (1), 154 , 2024 2024 Citations: 3
Numerical analysis of dermal cell-sheet wound healing model using b-spline collocation scheme N Rana, N Dhiman, R Singh 2024 15th International Conference on Computing Communication and Networking … , 2024 2024 Citations: 3
What resists millennials to adopt hotel booking apps? An empirical analysis based on extended innovation resistance theory S Kumar, N Dhiman, H Kanojia, R Joshi foresight 26 (1), 98-113 , 2024 2024 Citations: 3
Numerical approximation of the 3rd order pseudo-parabolic equation using collocation N Dhiman, M Tamsir, KA Aldwoah, MA Almalahi, W Adel 2024
Redefine trigonometric cubic B-spline collocation scheme for solving convection-diffusion equation AK Rawat, N Dhiman, A Chauhan, S Gupta International Journal of Computing Science and Mathematics 19 (3), 244-255 , 2024 2024
A hybrid B-spline collocation technique for the Caputo time fractional nonlinear Burgers’ equation M Tamsir, D Nigam, N Dhiman, A Chauhan Beni-Suef University Journal of Basic and Applied Sciences 12 (1), 95 , 2023 2023 Citations: 7
Finite Element Analysis of Two Disk Rotor System used in Automobile Turbochargers S Bhardawaj, AK Jha, RC Sharma, S Palli, D Lokanadham, N Sharma, ... International Journal of Vehicle Structures & Systems 15 (4), 501-504 , 2023 2023 Citations: 3
Dynamic behaviour of railway vehicle under bump and pothole track irregularities RC Sharma, S Palli, S Bhardawaj, AK Jha, A Duppala, N Sharma, ... International Journal of Vehicle Structures & Systems 15 (4), 566-569 , 2023 2023 Citations: 4
A CNN Approach to Detect Parkinson's Disease using T1-Weighted, T2-Weighted, and Flair MRI N Dhiman, R Singh, A Chauhan, A Bi 2023 Second International Conference on Augmented Intelligence and … , 2023 2023 Citations: 5
An inverse problem of identifying the time‐dependent potential in a fourth‐order pseudo‐parabolic equation from additional condition MJ Huntul, M Tamsir, N Dhiman Numerical Methods for Partial Differential Equations 39 (2), 848-865 , 2023 2023 Citations: 30
Convergence analysis and an efficient numerical technique for the solution of Benjamin Bona Mahony partial differential equation AK Rawat, G Deep, N Dhiman, A Chauhan International Journal of Mathematical Modelling and Numerical Optimisation … , 2023 2023 Citations: 3
Redefined quintic B-spline collocation technique for nonlinear higher order PDEs: M. Tamsir et al. M Tamsir, MJ Huntul, N Dhiman, S Singh Computational and Applied Mathematics 41 (8), 413 , 2022 2022 Citations: 5
Periodic orbits of circular restricted 3B problem N Dhiman International Conference on Advancements in Engineering and Sciences … , 2022 2022
Splines in vibration analysis of non-homogeneous circular plates of quadratic thickness R Singh, N Dhiman, M Tamsir Journal of Applied Analysis 28 (2), 263-273 , 2022 2022 Citations: 3
MOST CITED SCHOLAR PUBLICATIONS
Cubic trigonometric B-spline differential quadrature method for numerical treatment of Fisher’s reaction-diffusion equations M Tamsir, N Dhiman, VK Srivastava Alexandria engineering journal 57 (3), 2019-2026 , 2018 2018 Citations: 69
A collocation technique based on modified form of trigonometric cubic B-spline basis functions for Fisher’s reaction-diffusion equation N Dhiman, M Tamsir Multidiscipline Modeling in Materials and Structures 14 (5), 923-939 , 2018 2018 Citations: 54
Reconstructing an unknown potential term in the third-order pseudo-parabolic problem MJ Huntul, N Dhiman, M Tamsir Computational and Applied Mathematics 40 (4), 140 , 2021 2021 Citations: 42
Extended modified cubic B-spline algorithm for nonlinear Burgers' equation M Tamsir, N Dhiman, VK Srivastava Beni-Suef University journal of basic and applied sciences 5 (3), 244-254 , 2016 2016 Citations: 34
An inverse problem of identifying the time‐dependent potential in a fourth‐order pseudo‐parabolic equation from additional condition MJ Huntul, M Tamsir, N Dhiman Numerical Methods for Partial Differential Equations 39 (2), 848-865 , 2023 2023 Citations: 30
A modified trigonometric cubic B-spline collocation technique for solving the time-fractional diffusion equation N Dhiman, MJ Huntul, M Tamsir Engineering Computations 38 (7), 2921-2936 , 2021 2021 Citations: 30
Numerical computation of nonlinear Fisher’s reaction–diffusion equation with exponential modified cubic B-spline differential quadrature method M Tamsir, VK Srivastava, N Dhiman, A Chauhan International Journal of Applied and Computational Mathematics 4 (1), 6 , 2018 2018 Citations: 30
Approximation of Caputo time-fractional diffusion equation using redefined cubic exponential B-spline collocation technique M Tamsir, N Dhiman, D Nigam, A Chauhan AIMS Mathematics 6 (4), 3805-3820 , 2021 2021 Citations: 19
Identification of time-dependent potential in a fourth-order pseudo-hyperbolic equation from additional measurement ND M. J. Huntul, M. Tamsir Math. Methods Appl. Sci, doi: 10.1002/MMA.8104 , 2022 2022 Citations: 15
Solution of parabolic PDEs by modified quintic B-spline Crank-Nicolson collocation method M Tamsir, N Dhiman, A Chauhan, A Chauhan Ain Shams Engineering Journal , 2020 2020 Citations: 15
Numerical simulation of Fisher's type equation via a collocation technique based on re-defined quintic B-splines N Dhiman, A Chauhan, M Tamsir, A Chauhan Multidiscipline Modeling in Materials and Structures 16 (5), 1117-1130 , 2020 2020 Citations: 14
Re-modified quintic b-spline collocation method for the solution of Kuramoto–Sivashinsky type equations N Dhiman, M Tamsir Multidiscipline Modeling in Materials and Structures , 2018 2018 Citations: 13
Common fixed point theorem in M-fuzzy metric spaces using implicit relation SS Chauhan, N Joshi International Mathematical Forum 4 (47), 2311-2316 , 2009 2009 Citations: 11
A comprehensive study of fuzzy economic order quantity model with ramp type demand for perishable products AP Singh, A Chauhan, D Chauhan, D Patel, N Dhiman AIP Conference Proceedings 2481 (1), 040039 , 2022 2022 Citations: 9
DQM based on the modified form of CTB shape functions for coupled Burgers’ equation in 2D and 3D M Tamsir, N Dhiman Int. J. Math. Eng. Manag. Sci 4 (4), 1051 , 2019 2019 Citations: 9
Optimization of economic order quantity model with shortages having two parameter Weibull demand and deterioration rate under crisp and fuzzy system A Sayal, AP Singh, A Chauhan, N Dhiman AIP Conference Proceedings 2481 (1), 040031 , 2022 2022 Citations: 8
Optimized crisp and fuzzy inventory system of deteriorating items with partial backlogging under the effect of inflation A Sayal, AP Singh, A Chauhan, N Dhiman AIP Conference Proceedings 2481 (1), 040029 , 2022 2022 Citations: 8
An approximate analytical solution description of time-fractional order Fokker-Plank equation by using FRDTM N Dhiman, A Chauhan Asia Pacific J. Eng. Sci. Tech 1 (1), 34-47 , 2015 2015 Citations: 8
A hybrid B-spline collocation technique for the Caputo time fractional nonlinear Burgers’ equation M Tamsir, D Nigam, N Dhiman, A Chauhan Beni-Suef University Journal of Basic and Applied Sciences 12 (1), 95 , 2023 2023 Citations: 7
EOQ inventory model for ramp type demand without shortages under holding cost MK Sharma, M Kumar, R Verma, SJ Singh, N Dhiman AIP Conference Proceedings 2481 (1), 040034 , 2022 2022 Citations: 7
