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Aghalaya S. Vatsala

Aghalaya S. Vatsala
Pennzoil Endowed Professor
Applied Mathematics

406 Maxim Doucet Hall

Aghalaya S. Vatsala's webpage

Ph.D. 1973 Indian Institute of Technology, Madras
M.S. 1968 Bangalore University, Bangalore, India
B.S. 1966 Bangalore University, Bangalore, India

My main areas of research are ordinary and partial differential equations. My primary focuses are in the study of impulsive differential equations, reaction diffusion equations, differential equations with delay, integro-differential equations, singular systems and its applications. We develop numerical iterative procedures (yielding faster convergence) for the computation of solutions. Lyapunov stability theory, and stability in terms of two measures for large scale dynamical systems are my other major interests.

Selected research publications:

  • Subedi, Subhash and Vatsala, Aghalaya S., A quenching problem of Kawarada's type for one dimensional Caputo fractional reaction diffusion equation, Nonlinear Stud.,25 (2018) no. 3,505--519.
  • Chhetri, P. G. and Vatsala, A. S., Generalized monotone method for Riemann-Liouville fractional reaction diffusion equation with applications, Nonlinear Dyn. Syst. Theory, 18 (2018) no. 3,259--272.
  • Chhetri, Pradeep G. and Vatsala, Aghalaya S., The convergence of the solution of Caputo fractional reaction diffusion equation with numerical examples, Neural Parallel Sci. Comput., 25 (2017) no. 2,295--305.
  • Setia, Amit and Prakash, Bijil and Vatsala, A. S., Numerical solution of fourth order fractional integro-differential equation by using Legendre wavelets, Neural Parallel Sci. Comput., 23 (2015) no. 2-4,377--385.
  • Sambandham, Bhuvaneswari and Vatsala, Aghalaya S., Numerical results for linear Caputo fractional differential equations with variable coefficients and applications, Neural Parallel Sci. Comput., 23 (2015) no. 2-4,253--265.
  • Ram\'\irez, J. Diego and Vatsala, Aghalaya S., Generalized monotone iterative techniques for Caputo fractional integro-differential equations with initial condition, Neural Parallel Sci. Comput., 23 (2015) no. 2-4,219--237.
  • Marinov, Tchavdar T. and Marinova, Rossitza S. and Vatsala, Aghalaya S., Coefficient identification in Euler-Bernoulli equation from over-posed data, Neural Parallel Sci. Comput.,23 (2015) no. 2-4,193--218.
  • Vatsala, Aghalaya S. and Sowmya, M. and Stutson, Donna S., Generalized monotone method for ordinary and Caputo fractional differential equations, Dynam. Systems Appl., 24 (2015) no. 4,429--437.
  • Sowmya, M. and Vatsala, A. S., Generalized iterative methods for Caputo fractional differential equations via coupled lower and upper solutions with superlinear convergence, Nonlinear Dyn. Syst. Theory, 15 (2015) no. 2,198--208.
  • Anderson, Vinchencia and Bettis, Courtney and Brown, Shala and Davis, Jacqkis and Tull-Walker, Naeem and Chellamuthu, Vinodh and Vatsala, Aghalaya S. Superlinear convergence via mixed generalized quasilinearization method and generalized monotone method, Involve, 7 (2014) no. 5,699--712.