Numerical solution of boundary value problems for ordinary differential equations.

*(English)*Zbl 0671.65063
Prentice Hall Series in Computational Mathematics. Englewood Cliffs, NJ: Prentice-Hall, Inc. xxi, 595 p. $ 86.95 (1988).

This text is a comprehensive treatment of the numerical solution of boundary value problems for ordinary differential equations, suitable for graduate students and research workers with interests in the field. The book deals with both basic theory and practice, with some practical case studies, and includes on recent developments in the area.

The first three chapters provide a background in ordinary differential equations, boundary value problems and numerical analysis. This is followed by chapters dealing with finite difference methods and with methods based on techniques for solving initial value problems. The next chapter is devoted to decoupling and then there are chapters on the numerical treatment of linear and nonlinear systems of equations resulting from the discretization of boundary value problems. After a chapter dealing with mesh selection there are two final chapters on current research, in particular, on the singular perturbation problem, and on related topics.

There are historical notes and references for each chapter and an extensive bibliography. There are many illustrative examples and a good selection of exercises at the ends of the principal chapters. This book covers a considerable amount of material and should be very useful both as a graduate text and as a general reference work in the field.

The first three chapters provide a background in ordinary differential equations, boundary value problems and numerical analysis. This is followed by chapters dealing with finite difference methods and with methods based on techniques for solving initial value problems. The next chapter is devoted to decoupling and then there are chapters on the numerical treatment of linear and nonlinear systems of equations resulting from the discretization of boundary value problems. After a chapter dealing with mesh selection there are two final chapters on current research, in particular, on the singular perturbation problem, and on related topics.

There are historical notes and references for each chapter and an extensive bibliography. There are many illustrative examples and a good selection of exercises at the ends of the principal chapters. This book covers a considerable amount of material and should be very useful both as a graduate text and as a general reference work in the field.

Reviewer: G.J.Cooper

##### MSC:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

34Bxx | Boundary value problems for ordinary differential equations |

34E15 | Singular perturbations, general theory for ordinary differential equations |

65L05 | Numerical methods for initial value problems |