Research
I am a numericcal analyst specialising in Geometric Numerical Integration. I am currently working on the following research projects:
1) General Linear methods (GLMs):
- Construction of higher order G-symplectic GLMs (with Sarfraz Khan).
- GLMs preserving polynomial invariants via symmetric projection (with Lubna Mustafa)
2) Runge-Kutta methods (RK):
- Effective order of partitioned RK methods (with Muhammad Junaid, Saba Shafiq and John Butcher).
- Effective order of RK Nystrom methods (with Muhammad Junaid).
- Symplectic Effective order partitioned RK methods (with Azqa Arif).
- Hopf algebra of bicolour rooted trees and associated PRK group (composition of P-series)(with Saba Shafiq) .
The following research projects are available for PhD/MS students:
- Symplectic Effective order RK Nystrom methods.
- Analysis of Hopf algebra and Banach algebra in relation to bicolour rooted trees.
- Order Conditions for G-symplectic partitioned GLMs.
- Energy preserving GLMs.
Awards
- Overseas Scholarship from NUST/Government of Pakistan for PhD.
- Cambridge Commonwealth Scholarship from Cambridge University, UK for MS.
- Merit Scholarship from Punjab University for MSc. Mathematics.
- Presidential Scholarship from Govt. of Pakistan for BSc. Studies.
Conferences and Workshops
- 4th Seminar on Differential Equations, Dynamical Systems and Applications, (Invited Speaker) Mathematics Department, Zanjan, Iran. 17-19 July 2018.
- New Interactions of Combinatorics and Probability. (participant) CIMPA-Brazil research school, Universidade de Sao Paulo, Sao Carlos, Brazil. August 24 – September4, 2015.
- 6^{th} International Conference on Recent Developments in Fluid Mechanics(organizer) School of Natural Sciences, NUST, Islamabad, Pakistan. March 17-19,2015.
- MATLAB Optimization Tool Box Workshop (organizer and resource person)School of Mechanical and Manufacturing Engineering, NUST, Islamabad, Pakistan. April 14, 2014.
- NZMASP, New Zealand Mathematics and Statistics Postgraduate Conference (participant). Awarded People Choice Award for the presentation. Foxton Beach, New Zealand. November 23-26, 2009.
- PRIMA, Pacific Rim mathematical Association Congress (participant) University of New South Wales, Sydney, Australia. July 6-10, 2009.
- SciCADE, International Conference on Scientific Computation and Differential Equations (participant). Chinese Academy of Sciences, Beijing, China. May 25-29, 2009.
- GLADE, International Conference on General Linear Methods For Differential Equations (organizer). University of Auckland, New Zealand. July 14-18, 2008.
- NZMASP, New Zealand Mathematics and Statistics Postgraduate Conference (participant). University of Canterbury, Christchurch, New Zealand. December 12 - 15, 2007.
- AMS – NZMS, First Joint Conference of American Mathematical Society and New Zealand Mathematical Society. (participant). Victoria University of Wellington, New Zealand. December 12-15, 2007.
Research Supervisions
- Lubna Mustafa (MPhil Mathematics - in progress)
- Sarfraz Khan (MPhil Mathematics - in progress)
- Muhammad Junaid (Co-supervisor) (PhD Mathematics – in progress)
- Saba Shafique (MPhil Mathematics - thesis writing)
- Azqa Arif (MPhil Mathematics – thesis writing)
- WajeehaIrshad(MPhil Mathematics - 2017)
- Amber Masood (MPhil Mathematics 2015)
- Samina Ashraf (MPhil Mathematics 2014)
- Rabia Aziz (MPhil Mathematics 2013)
- Rafay Mustafa(MPhil Mathematics 2013)