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Research Projects

1. Parabolic problems for strongly elliptic operators on non-smooth domains: global regularity and numerical approximations by finite element, boundary element and spectral methods.
Theory, design, implementation of the non-standard finite difference method and applications to various directions: dynamical systems, conservation laws, singular pertubation problems, non-smooth mechanics, epidemiology models etc. 

Sponsors:

Abdus Salam International Centre for Theoretical Physics (Italy)(ICTP)
National Research Foundation (NRF):Unlocking the Future
UP Research Development Programme (RDP)
 
Leader and associated staff:
Prof JM-S Lubuma, Dr AR Appadu, Prof R Anguelov, Dr M Chapwanya, Dr PWM Chin, Dr J Djoko Kamdem, Dr SM Garba, Dr EW Mureithi, Prof EE Rosinger, Dr JH van der Walt
 
Involved PhD and/or MSc students with their supervisors (past 5 years)
AJ Matusse (MSc): Dr M Chapwanya (Supervisor)
N Mphepu (MSc): Dr AR Appadu (Supervisor)
M Mohamed (PhD): Dr J Djoko Kamdem (Supervisor)
H Gidey (PhD): Dr AR Appadu (Supervisor), Dr J Djoko Kamdem (Co-superisor)
OA Jejeniwa (PhD): Dr M Chapwanya (Supervisor), Dr AR Appadu (Co-supervisor) 
AA Aderogba (PhD):  Dr J Djoko Kamdem & Dr S Chapwanya (Co-supervisors)
P Chin (2001-2011):  Prof JM-S Lubuma (Supervisor), Dr KC Patidar (Co-supervisor)
P Kama (2002-2009):  Prof JM-S Lubuma (Supervisor)

 2. Biomathematics:

  • Mathematics motivated by biological applications: dynamical systems, PDEs, impulsive PDEs, interval analysis, validated numerics, nonstandard finite difference method, image analysis.
  • Mathematical epidemiology of human infectious diseases: modelling, analysis, reliable numerics and impact on health policy
Sponsor:
National Research Foundation (NRF)
Leader and associated staff:
Prof JM-S Lubuma, Prof R Anguelov, Dr SM Garba, Dr HM Djouosseu Tenkam (Postdoctoral Fellow), Dr Berge Tsanou (Postdoctoral Fellow)
Involved PhD and/or MSc students with their supervisors (past 5 years)
P Sivakumaran (MSc): Prof R Anguelov (Supervisor)
SM Stolz (MSc): Prof R Anguelov (Supervisor)
UA Danbaba (MSc):  Dr SM Garba (Supervisor)
CC Dufourd (PhD):   Prof R Anguelov (Supervisor), Prof Y Dumont (Co-supervisor)
Y Adane Terefe (PhD):  Prof JM-S Lubuma (Supervisor), completed MSc in 2012
AS Hassan (PhD):  Prof JM-S Lubuma (Supervisor), Dr SM Garba (Co-supervisor)
S Usaini (PhD):  Prof R Anguelov (Supervisor) Dr SM Garba (Co-supervisor)

3. Order and convergence theoretic methods for nonlinear PDE’s

Sponsor:
National Research Foundation (NRF)
Leader and associated staff:
Prof R Anguelov, Prof EE Rosinger, Dr JH van der Walt
Involved PhD and/or MSc students with their supervisors (past 5 years):
FD Agbebaku (PhD): Dr JH van der Walt (Supervisor), completed MSc in 2011

See also Universal PDE solution space

4. Image analysis

Sponsor:
Council for Scientific and Industrial Research (CSIR)
Leader:
Prof R Anguelov
Involved PhD and/or MSc students with their supervisors (past 5 years):
IN Fabris-Rotelli (completed PhD in 2012): Prof R Anguelov (Supervisor)

5. Mathematics education

  • Assessment
  • Visualisation
  • Transition to University
  • Conceptual and procedural thinking
  • Web-based teaching
  • Trends in enrolment
  • Conceptions about mathematics

Sponsors:
National Research Foundation (NRF)
Swedish International Development Cooperation Agency (SIDA)
Leader and associated staff:
Prof AF Harding, Ms A Verwey, Mrs K Bothma, Mrs Y Dinga, Mr HZ Wiggins, Mrs B Yani
Involved PhD and/or MSc students with their supervisors (past 5 years):     
T Masimura (MSc):  Prof AF Harding (Supervisor)
MD Madibane (MSc):  Prof AF Harding (Supervisor), Prof JC Engelbrecht (Co-supervisor)
A Billman (MSc):  Prof AF Harding (Supervisor), Prof JC Engelbrecht (Co-supervisor)
K Bothma (MSc):  Prof AF Harding (Supervisor), Prof JC Engelbrecht (Co-supervisor)
HZ Wiggins (PhD):  Prof AF Harding (Supervisor), Prof JC Engelbrecht (Co-supervisor), Prof WL Fouché (Co-supervisor)
BM Yani (PhD):  Prof AF Harding (Supervisor), Prof JC Engelbrecht (Co-supervisor)
BLK Mofolo-Mbokane (completed PhD in 2011): Prof JC Engelbrecht (Supervisor), Prof AF Harding (Co-supervisor)

6. Zeros of orthogonal polynomials

Sponsors:

National Research Foundation (NRF): Thuthuka Grant
KIC Grant University of Pretoria (ad hoc grant)
Abdus Salam International Centre for Theoretical Physics (Italy) (ICTP)
Postdoctoral Fellowship (UP)

Leader and associated staff:
Prof KH Jordaan, Dr AS Jooste, Dr P Gochhayat (Postdoctoral Fellow)
Involved PhD and/or MSc students with their supervisors (past 5 years):
MY Legesse (MSc): Prof KH Jordaan (Supervisor) AS Jooste (Co-supervisor)
AS Kelil (PhD): Prof KH Jordaan (Supervisor)
Lindie du Toit (completed MSc in 2012):  Prof KH Jordaan (Supervisor)
AS Jooste (completed PhD in 2012):  Prof KH Jordaan (Supervisor)
N Mbuyi Cimwanga (completed PhD in 2009): Prof KH Jordaan (Supervisor) Prof Kathy Driver (Co-supervisor)  

7.The Radon-Nikodym Property (RNP) for tensor norms as well as the operator space analogue of the RNP

Leader:
Dr SM Maepa
Involved PhD and/or MSc students with their supervisors (past 5 years):
CB Ndumba (PhD): Dr SM Maepa (Supervisor)
OD Arogunjo (PhD): Dr SM Maepa (Supervisor)

8. Computational finance; Option replication methods; Market risk management & metrics

  • Computational finance;
  • Option replication methods;
  • Market risk management & metrics

Sponsor:
UP Research Development Programme (RDP)
Leader and associated staff:
Prof E Maré, Dr R Kufakunesu, Dr AJ van Zyl
Involved PhD and/or MSc students (past 5 years):
Supervisor: Prof E Maré
B Feugang Nteumangne (PhD),
AK Ah Goo (MSc), F Babi (MSc), IP Barnett (MSc), RO Buhr (MSc):  Prof E Maré, P Diniz de Moura (MSc), MD Gonese (MSc), A Jordaan (MSc), C Kairinos (MSc), L Kelatwang(MSc), IM Lane (MSc), P Mentis (MSc), AM Ngugi (MSc), AGS Onanena (MSc), V Pataka (MSc), RB Rice (MSc), TC Sebolai (MSc), R Sivnarain (MSc), BH Taljaard (MSc), JB van Biljon (MSc), F Youbi (MSc)
L Mabitsela (MSc): Dr R Kufakunesu  (Supervisor)
CO Britz (MSc):  Prof E Maré (Supervisor), Dr AJ van Zyl  (Co-supervisor)

Completed MSc degrees
A Ostaszewicz (2012): Dr AJ van Zyl (Supervisor), PF du Preez (2011): Prof E Maré (Supervisor), KV Klynsmith (2011): Prof E Maré (Supervisor), WC Kuys (2011): Prof E Maré (Supervisor), SJ le Roux (2009): Prof E Maré (Supervisor), C Milwidsky (2011): Prof E Maré (Supervisor), N Simpson (2011): Prof E Maré (Supervisor), PJ, Erasmus (2010): Prof E Maré (Supervisor), S Hariparsad  (2009): Prof E Maré (Supervisor)

9. Non-Archimedean mathematics: From fundamental science to applications 

Sponsor:
Swedish International Developement Cooperation Agency (SIDA)
Leader and associated staff:
Prof EE Rosinger, Dr JH van der Walt, Dr AJ van Zyl, Dr DV Moubandjo

10.Symplectic algebra via sheaf theory  

Leader and associated staff:
Dr PP Ntumba, Dr SM Maepa
Involved PhD and/or MSc students with their supervisors (past 5 years):
RM Mayala (MSc): Dr PP Ntumba (Supervisor)
BY Yizengaw (PhD): Dr PP Ntumba (Supervisor), completed MSc in 2012
C Ndipingwi (PhD): Dr PP Ntumba (Supervisor)
AC Anyaegbunam (completed PhD in 2010):  Dr PP Ntumba (Supervisor)

11. Finite geometries 

Sponsor:
National Research Foundation (NRF)
Associated staff:
Prof I Broere, Ms L du Toit, Mr MDV Matsoha, Prof LM Pretorius

Involved PhD and/or MSc students with their supervisors (past 5 years)
MDV Matsoha (PhD): Prof I Broere (Supervisor), completed MSc in 2013  
L du Toit (PhD): Dr T Vetrik (Supervisor), Prof I Broere (Co-supervisor)

12. Stochastic models of fluid dynamics 

Sponsor:
National Research Foundation (NRF): Unlocking the future
Leader and associated staff:
Prof M Sango, Dr G Deugoue (Postdoctoral Fellow: 2011-2013), Dr P  Razafimandimby (Postdoctoral Fellow: 2011-2013), Dr C Tadmon (Postdoctoral Fellow: 2011-2013), Dr JL Woukeng Feudjio (Postdoctoral Fellow: 2010-2012)
Involved PhD and/or MSc students with their supervisors (past 5 years):
CA Emereuwa (MSc): Prof M Sango (Supervisor) 
ZI Ali (PhD): Prof M Sango (Supervisor), completed MSc in 2011
MAY Mohammed (PhD): Prof M Sango (Supervisor)
TA Tegegn (PhD): Prof M Sango (Supervisor) 
Dr G Deugoue (completed PhD in 2010): Prof M Sango (Supervisor)
Dr P Razafimandimby (completed PhD in 2010): Prof M Sango (Supervisor)

13. Equations of evolution 

Sponsor:
National Research Foundation (NRF)
Associated staff:
Prof N Sauer, Mr WS Lee
Involved PhD and/or MSc students with their supervisors (past 5 years):
WS Lee (PhD): Prof N Sauer (Supervisor), Prof A Ströh (Co-supervisor)    
S Dziwa (MSc): Prof N Sauer (Supervisor)
MB Nene (completed MSc in 2013): Prof N Sauer (Supervisor)

14. Noncommutative ergodic theory and quantum dynamical systems  

Sponsor:
National Research Foundation (NRF)
Leader and associated staff:
Prof A Ströh, Mr MB King
Involved PhD and/or MSc students with their supervisors (past 5 years):
MB King (MSc): Prof A Ströh (Supervisor), Dr RdV Duvenhage (Co-supervisor) 
MM Snyman (completed MSc in 2013): Dr RdV Duvenhage (Supervisor), Prof A Ströh (Co-supervisor)
DW van Wyk (Completed MSc in 2014): Dr R Duvenhage (Supervisor), Prof A Ströh (Co-supervisor)

15. Abstract analysis and stochastics 

Sponsor:
National Research Foundation (NRF)
UP Research Development Programme (RDP)
Leader and associated staff:
Prof J Swart, Dr AJ van Zyl, Mr MT Richards
Involved PhD and/or MSc students with their supervisors (past 5 years):
MT Richards (MSc): Dr AJ van Zyl (Supervisor)
BM Yani (completed MSc 2012): Dr AJ van Zyl (Supervisor)    
RG Venter (completed PhD in 2010): Prof J Swart (Supervisor)     
AJ van Zyl (completed PhD in 2009): Prof J Swart (Supervisor) 
GI Fordred (completed PhD in 2009): Prof J Swart (Supervisor) 

16. Vibration analysis

Sponsor:
National Research Foundation (NRF)
Leader and associated staff:
Prof NFJ van Rensburg, Miss M Basson, Miss S du Toit, Ms B Stapelberg
Involved PhD and/or MSc students with their supervisors (past 5 years):
S du Toit (MSc): Prof NFJ van Rensburg (Supervisor) 
B Stapelberg (MSc): Prof NFJ van Rensburg (Supervisor)
JM van Niekerk (MSc): Prof NFJ van Rensburg (Supervisor)
RH Sieberhagen (PhD): Prof NFJ van Rensburg (Supervisor) 
M Basson (completed PhD in 2014): Prof NFJ van Rensburg (Supervisor), completed MSc in 2011
DJ Civin (completed MSc in 2010): Prof NFJ van Rensburg (Supervisor) 
M de Villiers (completed MSc in 2009): Prof NFJ van Rensburg (Supervisor) 

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Last edited by Magdalena OosthuizenEdit