Dr. Vinod Mishra

Basic Details


Dr. Vinod Mishra






Phone (O)






Educational Details

Educational Qualification

B.Sc. (Physics, Chemistry, Maths); M.Sc. (Maths); Ph.D. (Maths)



1. Regular teaching (UG & PG):

PG (M.Sc. Maths) teaching: Wavelet Analysis; Classical Mechanics; Fluid Dynamics; Theoretical Seismology

UG (B.E.) teaching: Applied & Engineering Mathematics; Numerical Analysis; Statistics & Operations Research
2. Five months of industrial exposure at Chandigarh, Dehradun and Patiala
3. Invited Lectures arranged (02): Prof. Oscar Joao Abdounur (2011, Brazil) & Prof. Bhudev Sharma (2015, USA)
4. Programs Organized (04): National Workshop- IWCM2006 as Chairman; National Seminar- NSSA2007 as Chairman; National Science Week 2014 (Quiz, Poster Presentation & Seminar) as Convener; Earth Day (Poster Competition & Seminar) 2022 as Convener; Earth Day (Quiz, Poster Competition & Seminar) 2023 as Convener
5. Formerly Head: Department of Mathematics, SLIET Longowal, for more than three years

Book Authored

Book authored

1. Reference-cum-Text Book:
Vinod Mishra, Theory of Transforms with Applications, Ane Books Pvt Ltd, New Delhi, 2017, Pages 370 (Hardcover) (Price Rs 1995/-)     ISBN 978-93-8546-260-3

Chapters: i) Fourier Series,ii) Continuous Fourier Transform, iii) Discrete and Fast Fourier Transforms, iv) Laplace Transform, v) Numerical Inverse Laplace Transform,vi) Mellin Transform, vii) Hankel Transform, viii) Legendre Transform and ix) Z Transform
Appendix   Bibliography   Index


2. Edited Book Chapters:
i) Vinod Mishra, Fibonacci Sequence: History and Modern Applications, in: History and Development of Mathematics in India (Proceedings of CHDM Kanchipuram, 2018), National Mission for Manuscript and DK Printword (P) Ltd, New Delhi, 2022 , pp. 155-180.   ISBN 978-93-80829-70-8

ii) Vinod Mishra and Narbda Rani, Magic Squares in Indian Mathematics: Constructions and Properties, in: Understanding Values and Ethics in Shrinking World (Proceedings of VICUVESW, Central University of Rajasthan, 2022), Bloomsbury Publishing, UK, 2022, pp. 12-21.  ISBN 978-93-54358-94-4

Professional Memebership

Professional Membership

1. Indian Mathematical Society (Life Member)
2. Calcutta Mathematical Society (Life Member)
3. Indian Society for Industrial and Applied Mathematics (Life Member)
4. Indian Society for History of Mathematics (Life Member)
5. American Mathematical Society (Annual;1997)
6. Vijnana Parishad of India (Life Member)



1. Member: Post Graduate Board of Studies in Mathematics of Kurukshetra University (two years)

2. Member: Board of Management, SLIET (Deemed University) (one year)

3. Ph.D. Research Scholar: Physical Research Laboratory, Ahmedabad (August-October 1992)

4. Fellow (after Ph.D.; independent): Indian Institute of Advanced Study, Shimla (Nov. 1999-Nov. 2000).  Member (ex officio): Indian Institute of Advanced Study Society, Shimla (Nov. 1999-Nov. 2000)

5. Chief Guest & Keynote Speaker, “One Day State Level Workshop on Ramanujan and Development of Mathematics” Organized by Department of Mathematics, Government Kamladevi Rathi Girls PG College, Rajnandgaon (CG) on 21 December, 2021(Supported by Chhattisgarh Council of Science and Technology and National Council for Science and Technology Communication, DST, New Delhi)

6. Invited Lectures/Talks delivered  during national and international conferences on History of Mathematics/Wavelet Analysis/Numerical Laplace Transform) (finance born by host institutions): [29] including at:


Institutes of National Importance:

National Centre for Mathematics Mumbai (IITB-TIFR Joint Venture) (2013); IIT Bombay (2015); NIT Manipur (2016); Indian Institute of Advanced Study Shimla (2000); Inter-University Centre for Astronomy & Astrophysics Pune (1999)
Central & State Universities:

Jawaharlal Nehru University New Delhi (2020); HNB Garhwal University Srinagar (2016); Sikkim University Gangtok (2018); Bundelkhand University Jhansi (2018); Vikram University Ujjain (2021); Central University of Rajasthan, Ajmer (2022)
Deemed Universities:

Gurukula Kangri Vishwavidyalaya Haridwar (1998, 2003 & 2020); Sri Chandrasekhrendra Saraswathi Viswa Mahavidyalaya Kanchipuram (2018); Graphic Era University Dehradun (2011 & 2013); Sant Longowal Institute of Engineering & Technology Longowal (2013, 2019 & 2023)

PG Colleges:

DAV (PG) College Kanpur (2011 & 2022); Govt. Autonomous Digvijay (PG) College Rajnandgoan (2014)

Overseas Universities:

Tribhuvan University Kathmandu (2013); National University of Singapore (2005)


7. Guest Lectures delivered: (a) 02 on Classical Mechanics at Chandigarh University (Punjab) for M.Sc. Students, (b) Vector Calculus (03) and Numerical Methods (03) at NIT Uttarakhand for B.Tech. Students, (c) Indian Geometry (01) at Kurukshetra University to M.Sc. (Mathematics) students

8. Technical Sessions Chaired (during National and International Conferences) [16]:

Indian Institute of Advanced Study, Shimla (2000); Graphic Era University, Dehradun (2011, 2013); DAV (PG) College, Kanpur (2011); Govt. Digvijay PG College, Rajnandgoan (2014); Sri Sai College of Engineering & Technology, Pathankot (2015); Asra College of Engineering and Technology, Sangrur (2016); HNB Garhwal University, Pauri Campus (2016); Sri Chandarsekrendara Saraswathi Viswa Mahavidyalaya, Kanchipuram (2018); Central University of Rajasthan, Ajmer (2022); SLIET, Longowal (2011, 2020 (four), 2023).

9. Reviewer-American Mathematical Society (Mathematical Reviews/MathSciNet), Springer Nature, Elsevier and MDPI




Selected publications with links (UGC CARE/SCOPUS/WOS/SCI-Expanded/ MathSciNet/ZbMATH/CrossRef/Semantic Scholar indexed journals)  are given below. Citations reported are nearly 475, H-index 12, and i10-index 15.

Areas of research and publications:

1. History and Development of Mathematics
2. Wavelet Analysis
3. Numerical Laplace Transform
4. Matrix Algebra, Number Theory & Cryptography

1.    Harpreet Kaur, R.C. Mittal and Vinod Mishra (2013): 
Haar Wavelet Approximation Solutions for the Generalized Lane Emden Equations Arising in Astrophysics, Computer Physics Communications  (Elsevier) 184, 2169-2177.     [SCI, IF-4.717; SJR, 1.729]   [Citations: 66] http://dx.doi.org/10.1016/j.cpc.2013.04.013
2.    Harpreet Kaur, R.C. Mittal and Vinod Mishra (2014):
Haar Wavelet Solutions of Nonlinear Oscillator Equations, Applied Mathematical Modelling (Elsevier) 38, 4958-4971. [SCI, IF-5.336; SJR, 1.876]  [Citations: 32]  http://dx.doi.org/10.1016/j.apm.2014.03.019
3.    R.C. Mittal, Harpreet Kaur and Vinod Mishra (2015):
Haar Wavelet Based Numerical Investigation of Coupled Viscous Burgers Equation, International Journal of Computer Mathematics  (Taylor & Francis) 92, 1643-1659.    [SCI, IF-1.750; SJR, 0.456]    [Citations: 25]  https://www.tandfonline.com/doi/full/10.1080/00207160.2014.957688
4.    Dimple Rani and Vinod Mishra and Carlo Cattani (2018):
Numerical Inversion of Laplace Transform based on Bernstein Operational Matrix, Mathematical Methods in the Applied Sciences (Wiley & Sons) 41, 9231-9243.   [SCI, IF-3.007; SJR, 0.666] [Citations: 11]
5.    Dimple Rani and Vinod Mishra and Carlo Cattani (2019):
Numerical Inverse Laplace Transform for Solving a Class of Fractional Differential Equations, Symmetry-Basel  (MDPI) 11, No. 530, 1-20. [SCI, IF-2.940; SJR, 0.33]   [Citations: 21]
6.    Dimple Rani and Vinod Mishra (2020):
Numerical Inverse Laplace Transform based on Bernoulli Polynomials Operational Matrix for Solving Nonlinear Differential Equations, Results in Physics (Elsevier) 16, No. 102836, 1-7. [SCI, IF-4.565; SJR, 0.45] [Citations: 33]   https://doi.org/10.1016/j.rinp.2019.102836
7.    Vinod Mishra and Dimple Rani (2020):
Laplace Transform Inversion using Bernstein Operational Matrix of Integration and its Application to Differential and Integral Equations, Proceedings of National Academy of Sciences – Mathematical Sciences (Springer) 130, No. 60, 1-29. [SCI, IF-0.626; SJR, 0.31]  [Citations: 06]
8.    Narbda Rani, Suvita Rani Sharma and Vinod Mishra (2022):
Grayscale and Colored Image Encryption Model using a Novel Fused Magic Cube, Nonlinear Dynamics (Springer) 108, 1773-1796.  [SCI, IF-5.741; SJR, 1.25]  [Citations: 12]   https://doi.org/10.1007/s11071-022-07276-y
9.    Narbda Rani, Vinod Mishra and Birmohan Singh (2023):
Piecewise Symmetric Magic Cube: Application to Text Cryptography, Multimedia Tools and Applications (Springer) 82, 19369–19391.  [SCI, IF-2.757; SJR, 0.716]   [Citations: 0]                      https://doi.org/10.1007/s11042-022-14153-8
10. Narbda Rani, Vinod Mishra and Suvita Rani Sharma (2023):
Image Encryption Model based on Novel Magic Square with Differential Encoding and Chaotic Map, Nonlinear Dynamics (Springer) 111, 2869-2893.  [SCI, IF-5.741; SJR, 1.25]  [Citations: 01]  

1.    Vinod Mishra and Sabina (2011):
Wavelet-Galerkin Solutions of Ordinary Differential Equations, International Journal of Mathematical Analysis (Hikari) 5, 407-424.       [SJR, 0.211] [Citations: 42]
2.    Vinod Mishra and Harpreet Kaur (2014):
Haar Wavelet Approach for Solving Nonlinear Differential and Integral Equations, Neural, Parallel and Scientific Computations 22, 421-430.  [SJR, 0.127]  [Citations: 0]
3.    Vinod Mishra and Dimple Rani (2016):
Newton-Raphson based Modified Laplace Adomian Decomposition Method for Solving Quadratic Ricatti Differential Equations, Matec Web of Conferences 57, 05001, 1-4.  [SJR, 0.130]  [Citations: 08] [WOS(CPCI)] 


4.    Dimple Rani and Vinod Mishra (2019):
Solving Linear Fractional Order Differential Equations by Chebyshev Polynomials based Numerical inverse Laplace Transform, Mathematics in Engineering, Science and Aerospace 10, 781-791. [SJR, 0.163] [Citations: 10]
5.    Devendra Chouhan, Vinod Mishra and H.M. Srivastava (2021):
Bernoulli Wavelet Method for Numerical Solution of Anomalous Infiltration and Diffusion Modeling by Nonlinear Fractional Differential Equations of Variable Order, Results in Applied Mathematics (Elsevier) 10, No. 100146, pp.1-13.  [SJR, 0.69]   [Citations: 21]   [WOS (ESCI)]    https://doi.org/10.1016/j.rinam.2021.100146
6.    Narbda Rani and Vinod Mishra (2022):
Behaviour of Powers of Odd Ordered Special Circulant Magic Squares, International Journal of Mathematical Education in Science and Technology (Taylor & Francis) 53, 1044-1062.  [SJR, 0.630] [Citations: 03]   https://doi.org/10.1080/0020739X.2021.1890846

7.    Narbda Rani and Vinod Mishra (2023):
Ways of Constructing Multiplicative Magic Cubes, Proceedings in Mathematics and Statistics (FIAM 2021) (Springer) 410, 79-86.               [SJR, 0.204]                                             [Citations: 0]      https://link.springer.com/book/10.1007/978-981-19-7272-0
8.    Roji Bala and Vinod Mishra (2022):
Narayana Matrix Sequence, Proceedings of the Jangjeon Mathematical Society 25, 427-434.  [SJR, 0.29]  [Citations:0]  


1.    Vinod Mishra and S.L. Singh (1996):
Theorem of Square on the Diagonal in Vedic Geometry and its Application, Indian Journal of History of Science (Indian National Science Academy/ Springer) 31, 157-166.   [Citations: 05]  [UGC Care]
2.    Vinod Mishra and S.L. Singh (1997):
First Degree Indeterminate Analysis in Ancient India and its Application by Vrasena, Indian Journal of History of Science (Indian National Science Academy/Springer) 32, 127-133.  [Citations: 02]  [UGC Care]  https://insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol32_2_3_VMishra.pdf
3.    Vinod Mishra and Sabina (2010):
Wavelet Solutions of Parabolic Equations, Matematika: Malaysian Journal of Industrial and Applied Mathematics (University of Technology Malaysia) 26, 61-69.      [Citations: 02] [WOS-ESCI]  https://matematika.utm.my/index.php/matematika/article/view/550/0
4.    Vinod Mishra and Sabina (2010):
Wavelet Solutions and Stability Analysis of Parabolic Equations, Journal of Indonesian Mathematical Society 16, 69-87.     [Citations: 0] [WOS-ESCI]   http://dx.doi.org/10.22342/jims.
5.    Vinod Mishra (2011):
Computing: A Modern Generalization of Ancient Technique, Indian Journal of History of Science (Indian National Science Academy/Springer) 46, 49-61. [Citations: 02]  [UGC Care]
6.    Dimple Rani and Vinod Mishra (2018):
Modified Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton-Raphson Formula, European Journal of Pure and Applied Mathematics 11, 202-214.     [Citations: 26]      [WOS-ESCI]    https://doi.org/10.29020/nybg.ejpam.v11i1.2645
7.    Dimple Rani and Vinod Mishra (2019):
Solutions of Volterra Integral and Integro-Differential Equations using Modified Adomian Decomposition Method, Journal of Applied Mathematics, Statistics and Informatics (University of Saint Cyril and Metodius/ DeGruyter) 15, 5-18.   [Citations: 20]  [WOS-ESCI]     https://doi.org/10.2478/jamsi-2019-0001

8. Narbda Rani and Vinod Mishra (2022):

Application of Magic Squares in CryptographyProceedings in Adaptation, Learning and Optimization (ICIVC 2021) (Springer) 15, 321-329.  [Citations: 02]   https://doi.org/10.1007/978-3-030-97196-0_26


1.    Vinod Mishra and S.L. Singh (1996):
Height and Distance Problems in Ancient Indian Mathematics, Ganita Bharati (Bulletin of Indian Society for History of Mathematics) 18, 25-30. [Citations: 02]    http://www.researchgate.net/profile/Vinod_Mishra15
2.    Vinod Mishra and S.L. Singh (1998):
Values of p from Antiquity to Ramanujan, Sugakushi Kenkyu (Journal of History of Mathematics Society of Japan), No. 157, 12-25.  [Citations: 03]
3.    Vinod Mishra and S.L. Singh (1999):
Incircumscribing Triangles & Cyclic Quadrilaterals in Ancient & Medieval Indian Geometry, Sugakushi Kenkyu (Journal of History of Mathematics Society of Japan), No. 161, 1-11. [Citations: 03]
4.    Vinod Mishra (2011):
Haar Wavelet Approach to Fluid Flow Between Parallel Plates, International Journal of Fluids Engineering 4, 403-410.  [Citations: 02]   https://www.ripublication.com/irph/volume/ijfev3n4.htm
5.    Vinod Mishra and Sabina (2011):
Wavelet-Galerkin Finite Difference Solutions of ODEs, The Electronic International Journal-Advanced Modeling and Optimization 13, 539-549.  [Citations: 05]  https://camo.ici.ro/journal/vol13/v13c13.pdf
6.    Harpreet Kaur, R.C. Mittal and Vinod Mishra (2011):
Haar Wavelet Quasilinearization Approach for Solving Nonlinear Boundary Value Problems, American Journal of Computational Mathematics 1, 176-182.  [Citations: 38]    https://doi.org/10.4236/ajcm.2011.13020
7.    Sabina and Vinod Mishra (2011):
Wavelets and the Evaluation of Filter Coefficients, International Journal of Mathematical Archive 2, 1776-1793.    [Citations: 02]  https://www.ijma.info/index.php/ijma/article/view/603
8.    Sabina and Vinod Mishra (2012):
Wavelet-Galerkin Solutions of One and Two Dimensional Partial Differential Equations, Journal of Emerging Trends in Computing and Information Sciences 3, 1373-1378. [Citations: 03] 
9.    Vinod Mishra, Harpreet Kaur and R.C. Mittal (2012):
Haar Wavelet Solutions of Certain Differential, Integral and Integro-differential Equations, International Journal of Applied Mathematics and Mechanics 8, 69-82.  [Citations: 30]  http://www.researchgate.net/profile/Vinod_Mishra15
10. Harpreet Kaur, R.C. Mittal and Vinod Mishra (2012):
Haar Wavelet Quasilinearization Approach for Solving Lane Emden Equations, International Journal of Mathematics and Computer Applications Research 2, 47-60.    [Citations: 07] 

11. Harpreet Kaur, Vinod Mishra and R.C. Mittal (2013):
Numerical Solution of a Laminar Viscous Flow Boundary Layer Equation using Uniform Haar Wavelet Quasi-linearization Method, World Academy of Science Engineering and Technology 79, 1410-1415. [Citations: 12] doi.org/10.5281/zenodo.1087368
12. Vinod Mishra (2014):
Review of Numerical Inversion of Laplace Transforms using Fourier Analysis, Fast Fourier Transform and Orthogonal Polynomials, Mathematics in Engineering, Science and Aerospace 5, 239-261.     [Citations: 05]   http://nonlinearstudies.com/index.php/mesa/article/view/1037
13. Vinod Mishra and Dimple Rani (2015):
Chebyshev Polynomial based Numerical Inverse Laplace Transform Solutions of Linear Volterra Integral and Integro-differential Equations, American Research Journal of Mathematics 1, 22-32.    [Citations: 04] https://www.arjonline.org/papers/arjm/v1-i1/4.pdf

14. Dimple Rani and Vinod Mishra (2017):
Approximation Solution of Boundary Value Problem with Bernstein Polynomial Laplace Decomposition Method, International Journal of Pure and Applied Mathematics 114, 823-833.                                         [Citations: 05]             https://doi.org/10.12732/ijpam.v114i4.12

15. Roji Bala and Vinod Mishra (2022):

Solutions of Equations , Examples and Counterexamples (Elsevier) 2, No. 100043; 1-4. [Citations: 0]    https://doi.org/10.1016/j.exco.2021.100043


Complete list of publications and citations are available at:




I. Fellow Project (Monograph) submitted at IIAS Shimla (2001) by me: History of Mathematics and Mathematical Education with Special Reference to India



(a) History and Development of Mathematics (Ancient, medieval and pre-modern mathematics)-My Ph.D. research area

(b) Wavelet Analysis (Wavelet Galerkin and Collocation techniques for nonlinear problems)-Research area of Ph.D. supervision

(c) Numerical Analysis and Simulation (Numerical Laplace transform inversion and Galerkin techniques for nonlinear problems)-Research area of Ph.D. supervision

(d) Matrix Algebra, Number Theory & Cryptography (Indeterminate analysis & modular forms; Fibonacci & Narayana like sequences; Magic squares & cubes; Cryptography)-Research area of Ph.D. supervision




1.  Sabina: Wavelet-Galerkin Technique for Solving Certain Numerical Differential Equations and Inverse Ill-posed Problems (Awarded: August 2012)

2. Harpreet Kaur: Haar Wavelet Technique for Solving Differential, Integral and Integro-differential Equations (Awarded: March 2015).
3. Dimple Rani:  Laplace Transform based Numerical Solutions of Certain Differential and Integral Equations (Awarded: December 2020).

4. Ph.D. Continue: Narbda Rani (2018), Roji Bala (February 2019), Pavitra (October 2021)and Drishti Rajput (January 2023)



Barktullah University (Bhopal, 2017), Rastrasant Tukoji Maharaj Nagpur University (Nagpur, 2019), Lovely Professional University (Jalandhar, 2020, 2021 & 2022), GBPUAT (Pantnagar, 2021)


Note: NET/GATE qualified scholars interested for pursuing Ph.D. in MATHEMATICS AND ITS INTERDISCIPLINARY  APPLICATIONS may approach me at email: mishravinod560@gmail.com