Solving Differential Equations in R
Springer Science & Business Media, Jun 6, 2012 - Computers - 248 pages
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.
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Chapter 2 Initial Value Problems
Chapter 3 Solving Ordinary Differential Equations in R
Chapter 4 Differential Algebraic Equations
Chapter 5 Solving Differential Algebraic Equations in R
Chapter 6 Delay Differential Equations
Chapter 7 Solving Delay Differential Equations in R
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A-stable Adams methods advection algorithm analytic solution Applied Mathematics approximation backward differentiation formulae bimd boundary conditions boundary value problems bvpcol BVPs bvptwp Cash-Karp coefficients computed constant DAEs daspk DDEs defined delay differential equations dependent variables described deTestSet differential algebraic equations diffusion dimens discretisation error Euler example explicit Runge-Kutta methods finite difference func function evaluations function(t gamd grid higher order implement implicit methods initial conditions initial value problems integration interval iteration Jacobian linear multistep methods lsoda lsode matrix Mazzia mebdfi mfrow non-stiff nonlinear NULL numerical methods numerical solution obtain order equations order methods ordinary differential equations output package deSolve parameter parms partial differential equations PDEs Petzold plot radau ReacTran Runge-Kutta methods scheme second order Sect seq(from Shampine Soetaert Software solver Solving Differential Equations spatial specified stability step stiff problems vector velocity xgrid xlab yend yguess yini ylab ylag