# Ryan I. Fernandes

**Ryan I. Fernandes**

Associate Professor of Mathematics

Department of Mathematics

+971 (0)2 607 5274

rfernandes@pi.ac.ae

Dr. Ryan I. Fernandes was awarded the PhD degree in Mathematics by the University of Kentucky, Lexington, Kentucky, USA in 1991. Earlier he earned the MS. and BSc degrees from University of Bombay in 1981 and 1979, respectively.

Dr. Fernandes began his academic teaching career in 1979 as a high school teacher in Goa, India and, on obtaining an MSc degree, moved up to teach at St. Xavier’s Higher Secondary section for three years. On being awarded a full tuition scholarship and teaching/research assistantship he joined the Department of Mathematics at the University of Kentucky, USA where he earned his PhD in Numerical Analysis & Scientific Computing. Thereafter, in 1991 he worked for two years as a postdoc in the Center for Computational Sciences and this experience landed him a tenure track assistant professor position at the Mississippi State University (1993).

However, after three years, due to family reasons, he decided to return back to Goa and served as a senior lecturer at his alma mater for about nine years but kept his passion for research work active continuing to collaborate and publish high quality research in international journals. In 2005, he was invited as a visiting professor by the Department of Mathematical and Computer Sciences, Colorado School of Mines. On completion of the assignment he migrated to Hamilton, New Zealand where he began teaching at Sacred Hearts Girls’ college for about a year following which he joined the Department of Mathematics at The Petroleum Institute in 2006 as an associate professor of mathematics. While at the Petroleum Institute, he served on several committees in various capacities and, in particular, as the Head of the Mathematics Department for two years (2013-2015). The Petroleum Institute became part of the Khalifa University of Science and Technology in 2017.

**Undergraduate**:

- MATH111 Calculus I
- MATH161 Calculus II
- MATH212 Calculus III
- MATH261 Differential Equations
- MATH361 Advanced Engineering Mathematics
- MATH365 Numerical Methods
- MATH461 Linear Algebra

**Graduate**:

- MEEG503 Applied Numerical Methods
- MEEG/CEEG 508 Advanced Engineering Analysis

- “Efficient Numerical Techniques for solving Nonlinear Systems of PDEs”
- “Extension of the ADI Technique to
*Arbitrary*Regions” - “Collocation Methods for Solving Convection-Dominated PDE Problems”

- B. Bialecki B. and R. I. Fernandes, Alternating direction implicit orthogonal spline collocation on arbitrary regions with inconsistent partitions,
*Numer. Algor*., v. 74 (2017), pp. 1083-1100. - B. Bialecki B. and R. I. Fernandes, A convergence analysis of orthogonal spline collocation for solving two-point boundary value problems without the boundary subintervals,
*Int. J. Numer. Anal. Modeling*, v. 13 (2016), pp. 383 – 402. - R. I. Fernandes, B. Bialecki and G. Fairweather, An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains,
*J. Comp. Phys*., v. 299 (2015), pp. 561 – 580. - B. Bialecki B. and R. I. Fernandes, Alternating direction implicit orthogonal spline collocation on non-rectangular regions,
*Adv. Appl. Math. Mech.*, v. 5 (2013), pp. 461 – 476. - R. I. Fernandes and G. Fairweather, An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems,
*J. Comp. Phys.,*v. 231 (2012), pp. 6248 – 6267. - R. I. Fernandes, B. Bialecki, G. Fairweather, Alternating direction implicit orthogonal spline collocation methods for evolution equations, in: M.J. Jacob, S. Panda (Eds.), Mathematical Modelling and Applications to Industrial Problems (MMIP-2011), Macmillan Publishers India Limited, 2011. pp. 3–11.
- K. Pani, G. Fairweather and R. I. Fernandes, ADI orthogonal spline collocation methods for parabolic partial integro-differential equations,
*IMA J. Numer. Anal*., v. 30 (2010), pp. 248 – 276. - Bialecki B. and R. I. Fernandes, An alternating direction implicit backward differentiation orthogonal spline collocation method for linear variable coefficient parabolic equations,
*SIAM J. Numer. Anal*., v. 47(2009), pp. 3429 – 3450. - Emamizadeh and R. I. Fernandes, A monotonicity result related to clamped triangular elastic membranes,
*Adv. Modeling and Optimization,*v. 11 (2009), pp. 247 – 252. - K. Pani, G. Fairweather and R. I. Fernandes, Alternating direction implicit orthogonal spline collocation methods for an evolution equation with a positive-type memory term,
*SIAM J. Numer. Anal*., v. 46 (2008), pp. 344 – 364. - Emamizadeh, R. I. Fernandes and M. Poshtan, Applications of rearrangements to nonlinear optimization problems,
*Adv. Modeling and Optimization,*v. 10 (2008), pp. 323 – 329. - Emamizadeh and R. I. Fernandes, Optimization of the principal eigenvalue of the onedimensional Schrödinger operator,
*EJDE,*v. 2008 (2008), pp. 1 – 11. - B. Bialecki and R. I. Fernandes, An alternating-direction implicit orthogonal spline collocation scheme for nonlinear parabolic problems on rectangular polygons,
*SIAM J. Sci.**Comput.*, v. 28 (2006), pp. 1054 – 1077. - B. Bialecki and R. I. Fernandes, An orthogonal spline collocation alternating direction implicit method for linear second order hyperbolic problems on rectangles,
*IMA J. Numer.**Anal.,*v. 23 (2003), pp. 693 – 718. - B. Bialecki and R. I. Fernandes, An orthogonal spline collocation alternating direction implicit Crank-Nicolson method for linear parabolic problems on rectangles,
*SIAM J.**Numer. Anal.,*v. 36 (1999), pp. 1414 – 1434. - R. I. Fernandes, Efficient orthogonal spline collocation methods for solving linear second order hyperbolic problems on rectangles,
*Numer. Math.,*v. 70 (1997), pp. 223 – 241. - R. D. Saylor and R. I. Fernandes, On the parallelization of a comprehensive regional scale air quality model,
*Atmospheric Environment,*v. 27A (1993), pp. 625 – 631. - B. Bialecki and R. I. Fernandes, Orthogonal spline collocation Laplace-modified and alternating direction collocation methods for parabolic problems on rectangles,
*Math.**Comp.*, v. 60 (1993), pp. 545 – 573. - R. I. Fernandes and G. Fairweather, Analysis of alternating direction collocation methods for parabolic and hyperbolic equations in two space variables,
*Numer. Methods Partial**Different. Equ.*, v. 9 (1993), pp.191 – 211. - R. I. Fernandes and G. Fairweather, An alternating direction Galerkin method for a class of second-order hyperbolic equations in two space variables,
*SIAM J. Numer. Anal.*, v. 28 (1991), pp. 1265 – 1281.