Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics, numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology.
Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals.
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations. The idea is to choose a finite-dimensional space of candidate solutions and a number of points in the domain, and to select that solution which satisfies the given equation at the collocation points.
Lloyd Nicholas Trefethen is an American mathematician, professor of numerical analysis and head of the Numerical Analysis Group at the Mathematical Institute, University of Oxford.
Leslie Fox was a British mathematician noted for his contribution to numerical analysis.
Michael James David Powell was a British mathematician, who worked in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge.
Endre Süli is a mathematician. He is Professor of Numerical Analysis in the Mathematical Institute, University of Oxford, Fellow and Tutor in Mathematics at Worcester College, Oxford and Adjunct Fellow of Linacre College, Oxford. He was educated at the University of Belgrade and, as a British Council Visiting Student, at the University of Reading and St Catherine's College, Oxford. His research is concerned with the mathematical analysis of numerical algorithms for nonlinear partial differential equations.
Ernst Hairer is a professor of mathematics at the University of Geneva known for his work in numerical analysis.
Peter Karl Henrici was a Swiss mathematician best known for his contributions to the field of numerical analysis.
In numerical analysis and scientific computing, the trapezoidal rule is a numerical method to solve ordinary differential equations derived from the trapezoidal rule for computing integrals. The trapezoidal rule is an implicit second-order method, which can be considered as both a Runge–Kutta method and a linear multistep method.
Desmond John Higham is an applied mathematician and Professor of Numerical Analysis the School of Mathematics at the University of Edinburgh, United Kingdom.
Linda Ruth Petzold is a professor of computer science and mechanical engineering at the University of California, Santa Barbara, where she is also listed as affiliated faculty in the department of mathematics. Her research concerns differential algebraic equations and the computer simulation of large real-world social and biological networks.
Foundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.
Peter John Olver is a British-American mathematician working in differential geometry.
Hans Zanna Munthe-Kaas is a Norwegian mathematician working at UiT The Arctic University of Norway and the University of Bergen. The main focus of is work lies in the area of computational mathematics in the borderland between pure and applied mathematics and computer science.
Antonella Zanna Munthe-Kaas is an Italian applied mathematician and numerical analyst whose research includes work on numerical integration of differential equations and applications to medical imaging. She is a professor and head of the mathematics department at the University of Bergen in Norway.
Jan S. Hesthaven is a Danish mathematician, currently Vice President for Academic Affairs at EPFL. He is Professor of Mathematics, holds the Chair of Computational Mathematics and Simulation Science (MCSS), and was appointed Vice President for Academic Affairs at EPFL. He is particularly known for contributions to the development, analysis and application of high-order accurate computational methods for time-dependent partial differential equations. He has also contributed substantially to the development of reduced order models and the application of neural networks and machine learning techniques to problems in science and engineering.
Charles William Clenshaw was an English mathematician, specializing in numerical analysis. He is known for the Clenshaw algorithm (1955) and Clenshaw–Curtis quadrature (1960). In a 1984 paper Beyond Floating Point, Clenshaw and Frank W. J. Olver introduced symmetric level-index arithmetic.
Assyr Abdulle was a Swiss mathematician. He specialized in numerical mathematics.
Rosemary Anne Renaut is a British and American computational mathematician whose research interests include inverse problems and regularization with applications to medical imaging and seismic analysis. She is a professor in the School of Mathematical and Statistical Sciences at Arizona State University.
