Professor Gladwell works in a variety of numerical analysis and scientific computation research areas - including ordinary differential equation initial and boundary value problems, mathematical software, and parallel computing - with an emphasis on developing tools to assist scientists and engineers with large-scale computing problems. His research has involved scientific computation for sintering and grooving of materials, diffusion-convection equations, waves generated by a semi-infinite plate, and chromosome synapsis in grasses.
Recently, he has worked on use of symbolic software for aiding the numerical solution of singularly perturbed boundary value ordinary differential equations, parallel codes for almost block diagonal systems, variable step Runge-Kutta-Nystrom algorithms for special second-order systems, integration of Hamiltonian systems, parallelization of numerical integration, and wavelet collocation for boundary value problems. He has been working with faculty members at the University of Manchester, Emory University and the Colorado School of Mines, with members of the Numerical Algorithms Group, and with former SMU graduate students at the Johns Hopkins University, Texas Instruments, Oakland University, the University of New Hampshire, the Polish Academy of Sciences, University of Texas at Dallas, Texas Women's University and Collin County Community College.
Professor Gladwell was a faculty member at the University of Manchester, UK, before joining SMU in 1987. He has consulted with Texas Instruments and with NAG, is Editor-in-Chief of the ACM Transactions on Mathematical Software, and an Associate Editor of the IMA Journal on Numerical Analysis and of Scalable Computing: Practice and Experience, and is the editor and author of seven research monographs and special journal issues. His recent research has appeared in journals such as ACM Transactions on Mathematical Software, Applied Numerical Methods, SIAM Review, Parallel Computing, Journal of Computational and Applied Mathematics, Computational Materials Science, International Journal of Numerical Methods in Engineering, Numerical Linear Algebra and its Applications, Philosophical Magazine (Series A), and Computers and Mathematics with Applications, Journal of Crystal Growth, and SIAM Review.