Published Papers:
H. Ahmad, M. Younis, H. Gundogdo, N. Barley, Vijay Kumar Patel, Proximal contractions for multivalued mappings with an application to 2D Volterra integral equations, Accepted for publication in the journal Mathematics, 2024, 12(23), 3716; https://doi.org/10.3390/math12233716, MDPI SCIE Index (2024) ISSN 2227-7390, IF 2.3.
Vijay Kumar Patel, V. Sharma, N. Kumar, A. K. Tiwari, An Efficient Method for Solving Lane-Emden Equation using Legendre Neural Network, Accepted for publication in Springer SCOPUS index (2024).
V. Sharma, Vijay Kumar Patel, Y. Sahu, M. Vyas, AgriTransformer: Synergizing Robust Deep Transformer model for Intelligent Farming, Accepted for publication in Springer SCOPUS index (2024).
Vijay Kumar Patel, Abhishekh, D. Kumar, N. Kumar, A Machine Learning Model for Solving Lane-Emden Equation using Legendre Wavelet Neural Network, Accepted for publication in Springer SCOPUS index (2024).
Abhishekh, D. Kumar, Vijay Kumar Patel, A New Moving Average Time Series Forecasting Model Using Frequency Approach in Fuzzy Environment, Accepted in Springer SCOPUS index (2024).
Vijay Kumar Patel, An efficient finite difference scheme for fractional partial differential equation arising in electromagnetic waves model, International Journal of Nonlinear Analysis and Applications, 14 (10) (2023), 163-178. 10.22075/IJNAA.2023.28651.3962.
Vijay Kumar Patel and Dhirendra Bahuguna, Numerical and approximate solutions for two-dimensional hyperbolic telegraph equation via wavelet matrices, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 92 (2022), 605-623, https://link.springer.com/article/10.1007/s40010-022-00779-8.
Vijay Kumar Patel and Dhirendra Bahuguna, An efficient matrix approach for the numerical solutions of electromagnetic wave model based on fractional partial derivative, Applied Numerical Mathematics, 169 (2021), 1-20, https://doi.org/10.1016/j.apnum.2021.06.007 .
Vijay Kumar Patel, Somveer Singh, Vineet Kumar Singh, Numerical Wavelets Scheme for Complex Partial Differential Equation arising from Morlet Continuous Wavelet Transform, Numerical Methods for Partial Differential Equations, 37(2) (2020), 1163-1199, ISSN 1098-2426 https://doi.org/10.1002/num.22572 .
Vinita Devi, Rahul Kumar Maurya, Vijay Kumar Patel, V. K. Singh, Lagrange Operational Matrix Method to Lane-Emden, Riccati’s and Bessel’s Equations, I. Journal of Applied and Computational Mathematics, 5:79, (2019), 1-30, https://doi.org/10.1007/s40819-019-0655-6.
Somveer Singh, Vijay Kumar Patel, Vineet Kumar Singh, Application of wavelet collocation method for hyperbolic partial differential equations via matrices, Applied Mathematics and Computation, 320 (2018), 407-424, https://doi.org/10.1016/j.amc.2017.09.043 .
Vijay Kumar Patel, Somveer Singh, Vineet Kumar Singh, Emran Tohidi, Two Dimensional Wavelets Collocation Scheme for Linear and Nonlinear Volterra Weakly Singular Partial Integro-Differential Equations, I. Journal of Applied and Computational Mathematics, 4:32, 2018, 1-27, ISSN 2199-5796 , IF https://doi.org/10.1007/s40819-018-0560-4 .
Somveer Singh, Vijay Kumar Patel, Vineet Kumar Singh, Convergence rate of collocation method based on wavelet for nonlinear weakly singular partial integro-differential equation arising from viscoelasticity, Numerical Methods for Partial Differential Equations, 34 (5) (2018), 1781-1798, ISSN 1098-2426, IF 3, https://doi.org/10.1002/num.22245 .
Vijay Kumar Patel, Vineet Kumar Singh, Eugene B. Postnikov, Application of Piecewise Expansion based on 2D Legendre Wavelets for Fractional Partial Differential Equation, International Journal of Pure and Applied Mathematics, 119 (16b) (2018), 5159-5167, https://acadpubl.eu/hub/2018-119-16/2/531.pdf.
Somveer Singh, Vijay Kumar Patel, Vineet Kumar Singh, Emran Tohidi, Application of Bernoulli Matrix Method for Solving Two-dimensional Hyperbolic Telegraph Equation with Dirichlet Boundary Conditions, Computers & Mathematics with Applications, 75(2018), 2280-2294, ISSN 1873-7668, IF 2.9, https://doi.org/10.1016/j.camwa.2017.12.003 .
Vijay Kumar Patel, Somveer Singh, Vineet Kumar Singh, Two-dimensional shifted Legendre polynomials collocation method for electromagnetic waves in dielectric media via almost operational matrices, Mathematical Methods in the Applied Sciences, 40 (2017) 3698-3717, ISSN 3023-5294, IF 2.1, https://doi.org/10.1002/mma.4257 .
S. Singh, Vijay Kumar Patel, Vineet Kumar Singh, Emran Tohidi, Numerical Solution of Nonlinear weakly Singular Partial Integro-differential Equation via Operational Matrices, Applied Mathematics and Computation, Vol. 298 (2017), 310-321, ISSN 0096-3003 , IF 3.5 https://doi.org/10.1016/j.amc.2016.11.012 .
Vijay Kumar Patel, Somveer Singh, Vineet Kumar Singh, Two-dimensional wavelet collocation method for electromagnetic waves in dielectric media, Journal of Computational and Applied Mathematics, 317 (2017) 307-330, ISSN 0377-0427 , IF 2.1 https://doi.org/10.1016/j.cam.2016.11.026 .
Somveer Singh, Vijay Kumar Patel, Vineet Kumar Singh, Operational Matrix Approach for the Solution of Partial Integro- differential Equation, Applied Mathematics and Computation, Vol 283 (2016), pages 195-207, ISSN 0096-3003 , IF 3.5 https://doi.org/10.1016/j.amc.2016.02.036 .
Communicated Papers:
Vijay Kumar Patel, A stable class of finite difference scheme for time-fractional partial differential equation, submitted for publication (2022+).
Vijay Kumar Patel, An unconditionally stable finite difference scheme for time-fractional partial differential equations arising in electromagnetic waves model, submitted for publication (2022+).
Vijay Kumar Patel, Shifted-Legendre operational matrix algorithm to multi-term fractional partial differential equation with space-time variable coefficients, submitted for publication (2022+).
