He received the degree of licentiat from Stockholm University in 1949, before taking a break from his studies to work at the Swedish Board of Computer Machinery (Matematikmaskinnämnden), working on (among other things) the early computer BESK, Sweden's first. During this time, he also worked with Carl-Gustaf Rossby on early numerical weather forecasts.
Dahlquist returned to Stockholm University to complete his Ph.D., Stability and Error Bounds in the Numerical Solution of Ordinary Differential Equations, which he defended in 1958, with Fritz Carlson and Lars Hörmander as his advisors.[2] As part of this work he introduced the logarithmic norm (also introduced by Russian mathematician Sergei Lozinskii the same year).
In 1959 he moved to the Royal Institute of Technology (KTH), where he would later establish what became the Department of Numerical Analysis and Computer Science (NADA) in 1962 (now part of the School of Computer Science and Communication), and become Sweden's first Professor of Numerical Analysis in 1963.[3] He helped establish the Nordic journal of numerical analysis, BIT, in 1961. In 1965 he was elected into the Royal Swedish Academy of Engineering Sciences (IVA).
SIAM Germund Dahlquist Prize, established 1995, "Awarded to a young scientist (normally under 45) for original contributions to fields associated with Germund Dahlquist, especially the numerical solution of differential equations and numerical methods for scientific computing".