*By Len Freeman, Nick Higham and Jim Nagy*.

Ian Gladwell passed away on May 23, 2021 at the age of 76. He was born in Bolton, Lancashire in 1944. He did his secondary education at Thornleigh College, Bolton and was an undergraduate at Hertford College, University of Oxford, from where he graduated with a B.A. Hons. in Mathematics in 1966. He did his postgraduate studies at the University of Manchester, gaining an MSc in Numerical Analysis and Computing in 1967 and a PhD in Numerical Analysis in 1970. He was the first PhD student of Christopher T. H. Baker (1939–2017).

Ian was appointed Lecturer in the Department of Mathematics at the University of Manchester in 1969 and progressed to Senior Lecturer in 1980. He was a member of the Numerical Analysis Group (along with Christopher Baker, Len Freeman, George Hall, Will McLewin, Jack Williams (1943–2015), and Joan Walsh (1932–2017)) who, together with colleagues at UMIST, made Manchester a major centre of numerical analysis activity from the 1970s onwards.

Ian’s research focused on ordinary differential equation (ODE) initial value problems and boundary value problems, mathematical software, and parallel computing, and he had a wide knowledge of numerical analysis and scientific computing. He was perhaps best known for his pioneering work on mathematical software for the numerical solution of ODEs, much of which was published in the NAG Library and in the journal *ACM Transactions on Mathematical Software*. A particular topic of interest for Ian was algorithms and software for the numerical solution of almost block diagonal linear systems, which arise in discretizations of boundary value problems for ODEs and partial differential equations.

More details on Ian’s publications can be found at his MathSciNet author profile (subscription required). It lists 55 publications with 19 co-authors, among which Richard Brankin, Larry Shampine, Ruth Thomas, and Marcin Paprzycki are his most frequent co-authors.

In his time at Manchester he collaborated with a variety of colleagues both inside and outside the department, and he was always ready to offer advice to students and colleagues across the campus on numerical computing (as evidenced by the common sight of people waiting outside his office door to be seen).

Ian was instrumental in setting up the Manchester Numerical Analysis Reports, a long-running technical report series to which he contributed many items.

Ian had a five-month visit to the Department of Computer Science at the University of Toronto in 1975. Links between the Manchester and Toronto departments were strong, and over the years numerical analysts made several visits in both directions.

In the mid 1980s, Ian was one of the first people in the UK to have an email address: igladwel@uk.ac.ucl.cs. His email account was on a computer at University College London (UCL), because UCL hosted a gateway between JANET, the UK computer network, and ARPANET in the USA. Ian kindly allowed Nick Higham and Len Freeman use of the account to communicate with colleagues in the US.

Ian had long-standing collaborations with the Numerical Algorithms Group (NAG) Ltd., Oxford. He contributed many codes and associated documentation to the NAG Library, principally in ordinary differential equations. In a 1979 paper in ACM Trans. Math. Software he wrote

“When the NAG library structure was designed in the late 1960s, it was decided to devote a chapter, named DO2, to the numerical solution of systems of ordinary differential equations and that this chapter would be contributed by members of the Department of Mathematics, University of Manchester, and in particular by J. E. Walsh, G. Hall, and the author.”

Ian was a long-term member of NAG and of the NAG Technical Policy Committee, and during 1986 he held a Royal Society/Science and Engineering Research Council Industrial Fellowship at NAG.

Nick Higham was taught by Ian in an upper level undergraduate course “Numerical Linear Algebra” that Ian was giving for the first time, in 1981. As an MSc student and PhD student he benefited greatly from Ian’s advice about how to think about and do research.

Ian moved to the Department of Mathematics at Southern Methodist University (SMU), Dallas, as a Visiting Associate Professor in 1987, which became a permanent position in 1988. He had collaborated during the 1980s with Larry Shampine, who was working at Sandia National Laboratories until he moved to the SMU Mathematics Department in 1986.

Ian served as chair of the department 1988–1994 and again in 1998. He was also Director of Graduate Studies from 2005–2008. Ian excelled in these roles as mentor, which is recognized by a PhD fellowship in his honor. Jim Nagy was extremely fortunate to have Ian as his first department chair in 1992; Ian mentored him during the challenging tenure-track years, advising on research, teaching and more, including extensive editing of his first successful grant proposals.

Ian wrote the book *Solving ODEs with MATLAB* (2003) with Larry Shampine and Skip Thompson, which was described as “an excellent treatment of the fundamentals for solving ODEs using MATLAB” in Mathematical Reviews. It is Ian’s most highly cited work, with around 900 citations on Google Scholar at the time of writing.

Ian served as editor for ten journals, including as Associate Editor (2002–2005) and Editor-in-Chief (2005–2008) of *ACM Transactions on Mathematical Software*, as Associate Editor of the *IMA Journal on Numerical Analysis* (1988–2007), and as Associate Editor of *Scalable Computing: Practice and Experience* (2005–2010). A special issue of the latter journal in 2009 was dedicated to him on the occasion of his retirement from SMU

Ian was a long-term member of the Institute of Mathematics and Its Applications, of which he was a Fellow, and the Society for Industrial and Applied Mathematics.

According to the Mathematics Genealogy Project, Ian had 23 PhD students, equally split between Manchester and SMU, with one jointly supervised at the University of Bari.