Numerical Methods for Initial Value Problems

Martin Hermann and Masoud Saravi
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Martin Hermann: Friedrich Schiller University, Institute of Applied Mathematics
Masoud Saravi: Islamic Azad University Nour Branch, Department of Mathematics

Chapter Chapter 7 in A First Course in Ordinary Differential Equations, 2014, pp 189-240 from Springer

Abstract: Abstract With this chapter, the numerical part of the book begins. Here, numerical methods for initial value problems of systems of first-order differential equations are studied. Starting with the concept of discretizing differential equations, the class of Runge-Kutta methods is introduced. The Butcher schemes of a variety of Runge-Kutta methods are given. Further topics are consistency, convergence, estimation of the local discretization error, step-size control, A-stability, and stiffness.

Keywords: Local Discretization Error; Classical Runge-Kutta Method; Lobatto IIIA Method; Absolute Stability; Midpoint Rule (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-81-322-1835-7_7

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