Karline Soetaert Jeff Cash - Solving Differential Equations in R

Solving Differential Equations in R; Preface; R as a Problem Solving Environment; About the Three Authors; Acknowledgment; References; Contents; Chapter 1 Differential Equations; 1.1 Basic Theory of Ordinary Differential Equations; 1.1.1 First Order Differential Equations; 1.1.2 Analytic and Numerical Solutions; 1.1.3 Higher Order Ordinary Differential Equations; 1.1.4 Initial and Boundary Values; 1.1.5 Existence and Uniqueness of Analytic Solutions; 1.2 Numerical Methods; 1.2.1 The Euler Method; 1.2.2 Implicit Methods; 1.2.3 Accuracy and Convergence of Numerical Methods.;Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.