# My Favorite ODE

Posted by Cleve Moler,

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.... read more >>

# Strang and Moler Video Course on Differential Equations

Posted by Cleve Moler,

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.... read more >>

# Tumbling Box ODE2

Posted by Cleve Moler,

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.... read more >>

# Discover e with a graphical experiment

Posted by Cleve Moler,

An interactive graphical experiment lets you discover the value of one of the most important numerical quantities in mathematics. ... read more >>

# MathWorks Logo, Part Four, Method of Particular Solutions Generates the Logo

Posted by Cleve Moler,

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. ... read more >>

# MathWorks Logo, Part Three, PDE Toolbox2

Posted by Cleve Moler,

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.... read more >>

# MathWorks Logo, Part Two. Finite Differences2

Posted by Cleve Moler,

After reviewing the state of affairs fifty years ago, I use classic finite difference methods, followed by extrapolation, to find the first eigenvalue of the region underlying the MathWorks logo.... read more >>

# MathWorks Logo, Part One. Why Is It L Shaped?

Posted by Cleve Moler,

MathWorks is the only company in the world whose logo satisfies a partial differential equation. Why is the region for this equation shaped like a capital letter L? ... read more >>

# Ordinary Differential Equations, Stiffness3

Posted by Cleve Moler,

Stiffness is a subtle concept that plays an important role in assessing the effectiveness of numerical methods for ordinary differential equations. (This article is adapted from section 7.9, "Stiffness", in Numerical Computing with MATLAB.) ... read more >>

# Ordinary Differential Equation Solvers ODE23 and ODE454

Posted by Cleve Moler,

The functions ode23 and ode45 are the principal MATLAB and Simulink tools for solving nonstiff ordinary differential equations.... read more >>