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 >>

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.... 続きを読む >>

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? ... 続きを読む >>

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.) ... 続きを読む >>

The functions ode23 and ode45 are the principal MATLAB and Simulink tools for solving nonstiff ordinary differential equations.... 続きを読む >>

MATLAB and Simulink have a powerful suite of routines for the numerical solution of ordinary differential equations. Today's post offers an introduction. Subsequent posts will examine several of the routines in more detail.... 続きを読む >>

Changing the value of a parameter in the equations that produce the famous Lorenz chaotic attractor yields nonlinear ordinary differential equations that have periodic solutions. ... 続きを読む >>