Mon premier blog

Solving Differential Equations in R by Karline Soetaert, Jeff Cash, Francesca Mazzia

Solving Differential Equations in R Karline Soetaert, Jeff Cash, Francesca Mazzia ebook
ISBN: 3642280692, 9783642280696
Page: 264
Format: pdf
Publisher: Springer

We came to the section where we learn to solve high order linear differential equations with constant coefficients. Mathematics plays an important role in many scientific and engineering disciplines. After going through this module, students will be familiar with the Euler and Runge-Kutta methods for numerical solution of systems of ordinary differential equations. In the course of trying to solve the field equations of a physical system, within some assumptions about its symetry, i managed to get a non-linear ODE involving only a single function of one variable, but still rather tough to handle : In the equation , x=x(r) is the unknown function to find, and p0, p1, p2 are KNOWN functions of r (that i didn't take the time to write down here, but are not too complicated functions). \[ D(y)=c_1b_1+\cdots+c_nb_n.\]. This book deals with the numerical solution of differential equations, a very important branch of mathematics. [ \forall_{c_1,\dots,c_n\in\mathbb{R}}(c_1y_1+\cdots+c_ny_n=0\;\Rightarrow\; c_1=\cdots=c_n=0).\]. This is sometimes called the superposition principle. Denote the left hand side of this equation then their linear combination, i.e.~any function of the form $c_1y_1+\cdots+c_ny_n$ where each $c_i$ is an arbitrary constant, is a solution of the differential equation. Consider a linear differential equation of order $n$, as above. We went over the characteristic polynomial, and the case where it has a repeated root.