Recently, I had email from a student in Italy.... 続きを読む >>

I am working with Indika Rajapakse and Steve Smale to investigate the stability of the dynamic system describing Kuramoto oscillators. Indika and Steve are interested in Kuramoto oscillators for two reasons; the self synchronization provides a model of the cells in a beating heart and the dynamic system is an example for Morse-Smale theory. I am personally interested in the Kuramoto model as it relates to deep brain stimulation (DBS) for open-loop control of human movement disorders. My kuramoto program demonstrates both stable and unstable critical points. Roundoff error may destabilize an unstable critical point.... 続きを読む >>

The ACM Special Interest Group on Programming Languages, SIGPLAN, expects to hold the fourth in a series of conferences on the History of Programming Languages in 2020, see HOPL-IV. The first drafts of papers are to be submitted by August 2018. That long lead time gives me the opportunity to write a detailed history of MATLAB. I plan to write the paper in sections, which I'll post in this blog as they are available.... 続きを読む >>

Three-term recurrence relations are the basis for computing Bessel functions. Contents A Familiar Three-Term Recurrence Friedrich Bessel Bessel Functions Miller's Algorithm ... 続きを読む >>

My favorite ordinary differential equation provides a good test of ODE solvers, both numeric and symbolic. It also provides a nice illustration of the underlying existence theory and error analysis.... 続きを読む >>

Gil Strang has produced a MOOC-style video course on Differential Equations and Linear Algebra. I have added some videos about the MATLAB ODE suite. The series is available from the MathWorks Web site, MIT OpenCourseWare and several other popular sources.... 続きを読む >>

A rectangular box, such as a book or a cell phone, thrown in the air can tumble stably about its longest axis, or about its shortest axis, but not about its middle axis.... 続きを読む >>

An interactive graphical experiment lets you discover the value of one of the most important numerical quantities in mathematics. ... 続きを読む >>

The Method of Particular Solutions computes a highly accurate approximation to the eigenvalue we have been seeking, and guaranteed bounds on the accuracy. It also provides flexibility involving the boundary conditions that leads to the MathWorks logo. ... 続きを読む >>

The Partial Differential Equation Toolbox contains tools for the analysis of PDEs in two space dimensions and time. It is perhaps not surprising that one of the primary examples involves the L-shaped membrane.... 続きを読む >>