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In science and engineering classes, you might describe a system using Newton’s laws and end up with a differential equation. You then solve the differential equation, analytically...
When you’re interested in studying a family of functions, it can be useful to look at a differential equation that the functions solve. This is a theme I’ve written about several t...
I was digging into the Runge-Kutta method for solving differential equations and a line from [1] piqued my curiosity. These calculations, which are not reproduced in Kutta’s paper...
Second order linear differential equations with polynomial coefficients form their own area of study. This seems like a narrow class of equations, but it’s very important in applic...
Yesterday I wrote that a lot of the special functions that pop up in mathematical physics are solutions to second order linear differential equations with polynomial coefficients....
This post provides a couple examples to go along with two earlier posts. The pattern we’re illustrating is families of polynomials pn(x) that each satisfy a differential equation a...
В рамках статьи рассматривается база, на основании которой строится семейство методов Рунге—Кутты, а также в одном моменте поднимается ограничение данного метода, вызванное огранич...
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