American Journal of Mathematics and Statistics

American Journal of Mathematics and Statistics is to publish well-written original research articles and studies describing the latest research and developments in the field of mathematics and statistics. This is a broad-based journal covering all branches of mathematics, statistics and interdisciplinary research.

Manoj Kumar

Editorial Board Member of American Journal of Mathematics and Statistics

Associate Professor, Department of Mathematics, Motilal Nehru National Institute of Technology, India

Research Areas

Numerical Analysis and Scientific Computing

Education

2000Ph.DApplied Mathematics, Aligarh M. University Aligarh, India
1997M.ScMathematics, Aligarh M. University Aligarh, India

Experience

2005-presentLecturer and Associate Professor, M.N. Institute of Technology, Allahabad
2005Lecturer, Govt. of NCT, Delhi
2001-2005Lecturer, College of Engineering, Roorkee

Membership

Life member of the Indian Mathematical Society (IMS)
Life member of the Ramanujan Mathematical Society (RMS)
Life member of the Indian Society of Industrial & Applied Mathematics (ISIAM)
Life member of the The National Academy of Sciences India (NASI)

Publications: Journals

[1]  Manoj Kumar (With Akanksha Srivastava): An Elementary Introduction to Recently Developed Computational Methods for Solving Singularly Perturbed Partial Differential Equations Arising in Science and Engineering. Accepted for publication in International Journal of Computational Methods in Engineering Science and Mechanics (Taylor & Francis Journal).
[2]  Manoj Kumar (With Parul): A Recent Development of Computer Methods for Solving Singularly Perturbed Boundary Value Problems, Accepted for publication in International Journal of Differential Equations (Hindawi Publication Journal).
[3]  Manoj Kumar (with Pankaj Kr Srivastava, R. Mohapatra): Quintic Nonpolynomial Spline Method for the Solution of a Second-Order Boundary-value Problem with engineering applications. Published in An International Journal "Computers and Mathematics with Applications" 62 (2011) 1707-1714 (Elsevier Journal).
[4]  Manoj Kumar (With Neelima Singh): Computer simulation of third order non-linear singular problems arising in draining and coating flows. Published in the International Journal for Numerical Methods in Fluids (2011), DOI: 10.1002/fld.2635 (Wiley Journal).
[5]  Manoj Kumar (With Parul): Methods for Solving Singular Perturbation Problems Arising in Science and Engineering, Published in An International Journal Mathematical and Computer Modelling 54 (2011) 556-575 (Elsevier Journal).
[6]  Manoj Kumar (With Pratibha Joshi): Some Numerical Techniques for Solving Elliptic Interface Problems, Published in Numerical Methods for Partial Differential Equations (2010), DOI: 10.1002/num.20609 (Wiley Journal).
[7]  Manoj Kumar (With Neelima Singh): Modified Adomian Decomposition Method and Computer Implementation for Solving Singular Boundary Value Problems Arising in Various Physical Problems, Published in An International Journal "Computers and Chemical Engineering 34 (2010) 1750-1760 (Elsevier Journal).
[8]  Manoj Kumar (With Prashant Kumar): Simulation of Non-linear Steklov Eigen Value Problem Using Finite Element approximation, Published in Computational Mathematics and Modeling Vol.21 number1 (2010) (Springer Journal).
[9]  Manoj Kumar (With Prashant Kumar): Computational Method for Finding Various Solutions for a Quasilinear Elliptic Equation of Kirchhoff Type, Published in Advances in Engineering Software Volume 40, Issue 11, November 2009, Pages 1104-1111 (Elsevier Journal).
[10]  Manoj Kumar (With Neelima Singh): A Collection of Computational Techniques for Solving Singular Boundary Value Problems. Published in Advances in Engineering Software Advances in Engineering Software, Volume 40, Issue 4, April 2009, Pages 288-297 (Elsevier Journal).
[11]  Manoj Kumar (with Pankaj Kr Srivastava): Computational Techniques for Solving Differential Equations by Cubic, Quintic and Sextic Spline. Published in International Journal of Computational Methods in Engineering Science & Mechanics, Volume 10, Issue 1, January 2009, pages 108-115 (Taylor & Francis Journal).
[12]  Manoj Kumar (With H.K.Mishra & P.Singh): Numerical Treatment of Singularly Perturbed Two-Point Boundary Value Problems using Initial-Value Method. Published in Journal of Applied Mathematics and Computing Volume 29, Numbers 1-2/January, 2009 pages 229-246 (Springer Journal).
[13]  Manoj Kumar (With H.K.Mishra & P.Singh): A Boundary Value approach for Singularly Perturbed Boundary Value Problems. Published in Advances in Engineering Software, Volume 40, Issue 4, April 2009, Pages 298-304 (Elsevier Journal).
[14]  Manoj Kumar (With Prashant Kumar): A finite element approach for finding positive solutions of semilinear elliptic Dirichlet problems. Published in Numerical Methods for Partial Differential Equations, 25:1119-1128(2009) (Wiley Journal).
[15]  Manoj Kumar (With P.Singh & H.K.Mishra): Initial-Value Technique for Self-Adjoint Singular Perturbation Boundary Value problems. Published in Computational Mathematics and Modeling Vol.20 number 2 (2009) (Springer Journal).
[16]  Manoj Kumar (With P.Singh & Prashant Kumar): A Various Computational Techniques for Non-linear Elliptic Boundary Value Problems. Published in Advances in Engineering Software 39/9(2008)725-736 (Elsevier Journal).
[17]  Manoj Kumar: Computational Technique for Singular Boundary Value Problems By Using Numerical Quadrature. Published in Computational Mathematics and Modeling 19/2(2008)195-200 (Springer Journal).
[18]  Manoj Kumar (With Yogesh Gupta): Methods for Solving Singular Boundary Value Problems Using Splines: A Survey, Accepted for publication in Journal of Applied Mathematics and Computing (Springer Journal).
[19]  Manoj Kumar(with Pankaj Kr Srivastava): Computational Techniques for solving differential equations by Quadratic, Quartic and Octic spline. Published in Advances in Engineering Software 39(2008)646-653 (Elsevier Journal).
[20]  Manoj Kumar: Higher Order Method for Singular Boundary Value Problems By Using Spline Function. Published in Applied Mathematics and computation 192(2007)175-179(Elsevier Journal).
[21]  Manoj Kumar (With P.Singh & H.K.Mishra): An Initial-Value Technique for Singularly Perturbed Boundary Value Problems via Cubic Spline. Published in International Journal of Computational Methods in Engineering Science & Mechanics 8(2007)1-9 (Taylor & Francis Journal).
[22]  Manoj Kumar (With P.Singh & H.K.Mishra): A Recent Survey on Computational Techniques for Solving Singularly Perturbed Boundary Value Problems. Published in International Journal of Computer Mathematics 84 (2007)1-25(Taylor & Francis Journal).
[23]  Manoj Kumar (With Tariq Aziz): A uniform mesh finite difference method for a class of singular two-point boundary value problems. Published in Applied Mathematics and computation180 (2006)173-177(Elsevier Journal).
[24]  Manoj Kumar (With Tariq Aziz): A non-uniform mesh finite difference method and its convergence for a class of singular two-point boundary value problems. Published in International Journal of Computer Mathematics 81(2004)1507-1512(Taylor & Francis Journal).
[25]  Manoj Kumar: A difference scheme based on non-uniform mesh for a class of singular two-point boundary value problems Published in Applied Mathematics and Computation136 (2003)281-288(Elsevier Journal).
[26]  Manoj Kumar: A second order spline finite difference method for singular two-point boundary value problems published in Applied Mathematics and Computation 142(2003)283-290(Elsevier Journal).
[27]  Manoj Kumar: A second order finite difference method and its convergence for a class of singular two-point boundary value problems Published in Applied Mathematics and Computation 146(2003)873-878(Elsevier Journal).
[28]  Manoj Kumar: A new finite difference method for a class of singular two-point boundary value problems Published in Applied Mathematics and Computation 143(2003)551-557(Elsevier Journal).
[29]  Manoj Kumar: A difference method for a class of singular two-point boundary value problems. Published In Applied Mathematics and Computation 146(2003) 879-884(Elsevier Journal).
[30]  Manoj Kumar: A fourth order spline finite difference method for a class of singular two-point boundary value problems. Published in International Journal of Computer Mathematics 80(2003)1499-1504(Taylor & Francis Journal).
[31]  Manoj Kumar: A three-point finite difference method for a class of singular two-point boundary value problems. Published in Journal of Computational and Applied Mathematics 145(2002)89-97(Elsevier Journal).
[32]  Manoj Kumar: A fourth-order finite difference method for a class of singular two-point boundary value problems. Published in Applied Mathematics and Computation 133(2002)539-545(Elsevier Journal).
[33]  Manoj Kumar (With Tariq Aziz): A fourth-order finite difference method based on non-uniform mesh for a class of singular two-point boundary value problems. Published in Journal of Computational and Applied Mathematics 136(2001)337-342(Elsevier Journal).

Publications: Conferences/Workshops/Symposiums

[1]  Manoj Kumar: Computational Techniques for Solving Singular Boundary Value Problems by Using Spline Function. Presented in International Conference "2nd International Congress on Computational Mechanics and Simulation" December 8-10, 2006 Indian Institute of Technology Guwahati, India.
[2]  Manoj Kumar (With H.K.Mishra): Pade Approximates for a Class of Nonlinear Singular Perturbation Problems, presented in the conference on "Modern Analysis and Allied Areas (23-24, February, 2007) at Department of Mathematics, Banaras Hindu University, Varanasi.
[3]  Manoj Kumar (With H.K.Mishra): Computational Techniques for Solving Singularly Perturbed Boundary Value Problem. presented in International Congress & 8th Conference of Indian Society of Industrial & Applied Mathematics (ISIAM) on Certain Emerging Areas in Applicable Mathematics and 17th Annual Conference of Jammu Mathematical Society to be held at Jammu University, Jammu (March 31-April,3).
[4]  Manoj Kumar (With Yogesh Gupta): "Computational Techniques for Solving Singular Perturbation Problems" Presented in International Conference On Modeling of Engineering & Technological Problems (ICMETP) And 9th National Conference of Indian Society of Industrial and Applied Mathematics at Agra during January 14-16, 2009.
[5]  Manoj Kumar (With Pankaj Kr Srivastava): "Use of Higher Order Splines for Solving Differential Equations" Presented in International Conference On Modeling of Engineering & Technological Problems (ICMETP) And 9th National Conference of Indian Society of Industrial and Applied Mathematics at Agra during January 14-16, 2009.
[6]  Manoj Kumar(With Neelima Singh):"Modified Adomian Decomposition Method and Its Symbolic Implementation for Singular Boundary Value Problems" presented in "International Conference on recent trends in Mathematics and its Applications" organized by Department of Mathematics, Jamia Millia Islamia (Central University) Delhi during March 30-31, 2009.
[7]  Manoj Kumar(With Neelima Singh): Modified Adomian Decomposition Method for Singular Boundary Value Problems Arising in various Physical Problems" presented in "24 Annual Conference of Ramanujan Mathematical Society organized by Department of Mathematics, Indian Statistical Institute, Bangalore during May 11-13, 2009.
[8]  Manoj Kumar (With Neelima Singh): Decomposition Technique for solving higher order Singular Boundary Value Problems, Presented in 11th International Conference of the International Academy of Physical Sciences, February 20-22, 2010, University of Allahabad
[9]  Manoj Kumar (With Pratibha Joshi): Numerical Solution of a Steady State Heat Conduction Problem using High Order Immersed Interface Method on Non-Uniform Mesh, Presented in 11th International Conference of the International Academy of Physical Sciences, February 20-22, 2010, University of Allahabad.
[10]  Manoj Kumar (With Anand Shukla): Monte Carlo Method for Solving Real Life Problems, Presented in 11th International Conference of the International Academy of Physical Sciences, February 20-22, 2010, University of Allahabad.
[11]  Manoj Kumar (With Pratibha Joshi): Numerical Simulation of Steady State Heat Conduction in Multi-Layered Bodies, Presented in National Conference on Recent Trends in Mathematical Modelling and Simulation (RTMMS-2010), March 18-20, 2010, organized by Deapartment of Applied Mathematics, Institute of Technology Banaras Hindu University, Varanasi.
[12]  Manoj Kumar (With Neelima Singh): Computer Simulation of Boundary Value Problems Arising in Science and Engineering, presented in National conference on Nonlinear analysis and applications organized by Department of Mathematics, H. N. B. Garhwal University,(A central university) Pauri Campus Pauri Garhwal 246001, Uttarakhand during 5‐7 June, 2010.
[13]  Manoj Kumar (With Akanksha Srivastava): Methods for Solving Singularly Perturbed Boundary Value Problems, presented in National conference on Nonlinear analysis and applications organized by Department of Mathematics, H. N. B. Garhwal University,(A central university) Pauri Campus Pauri Garhwal 246001, Uttarakhand during 5‐7 June, 2010.
[14]  Pankaj Kumar Srivastava, Manoj Kumar, R.N. Mohapatra: Quintic Non Polynomial Spline Method for the Solution of a Second Order Boundary Value Problem with Engineering Applications, presented in 26th annual conference of the mathematical society, Banaras Hindu University, Varanasi on "Recent Trends in Analysis and Modeling" organized by department of mathematics, faculty of science, Banaras Hindu University, Varanasi, during November 28-29, 2010.
[15]  Pratibha Joshi and Manoj Kumar: Thermal Analysis of Composite Systems with Imperfect Interface, presented in 26th annual conference of the mathematical society, Banaras Hindu University, Varanasi on "Recent Trends in Analysis and Modeling" organized by department of mathematics, faculty of science, Banaras Hindu University, Varanasi, during November 28-29, 2010.
[16]  Manoj Kumar and Neelima Singh: Numerical Simulation of Boundary Value Problems Arising in Engineering, presented in 4th International Conference on "Mathematical Sciences for Advancement of Science & Technology" organized by IMBIC and ISI Kolkata during 19-21 December, 2010, Kolkata.
[17]  Akanksha Srivastava and Manoj Kumar: A Recent Development of Various Computational Techniques for Solving Singularly Perturbed Partial Differential Equations, presented in 4th International Conference on "Mathematical Sciences for Advancement of Science & Technology" organized by IMBIC and ISI Kolkata during 19-21 December, 2010, Kolkata.
[18]  Manoj Kumar and Neelima Singh: Adomian Decomposition Method for Solving Higher Order Boundary Value Problems, Presented in Sixth International Conference on Dynamic Systems and Applications during May 25-28, 2011, Atlanta, Georgia, USA.
[19]  Manoj Kumar and Neelima Singh:Boundary Value Problems:Third and fourth order" Presented in 7th International Congress on Industrial and Applied Mathematics-ICIAM 2011, during July18-22 at Vancouver, BC, Canada.