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

1. Lubna Mustafa (MPhil Mathematics -  in progress)
2. Sarfraz Khan (MPhil Mathematics -  in progress)
3. Muhammad Junaid (Co-supervisor) (PhD Mathematics – in progress)
4. Saba Shafique (MPhil Mathematics -  thesis writing)
5. Azqa Arif (MPhil Mathematics – thesis writing)
6. WajeehaIrshad(MPhil Mathematics -  2017)
7. Amber Masood (MPhil Mathematics 2015)
8. Samina Ashraf (MPhil Mathematics 2014)
9. Rabia Aziz          (MPhil Mathematics 2013)
10. Rafay Mustafa(MPhil Mathematics 2013)