Numerical Methods for Solving Two-Point BoundaryValue Problems: Differed Correction Schemes, Interpolation, and Conditioning Methods - Tapa blanda

Sumarti, Novriana

 
9783639137873: Numerical Methods for Solving Two-Point BoundaryValue Problems: Differed Correction Schemes, Interpolation, and Conditioning Methods
Tapa blanda
ISBN 10: 3639137876 ISBN 13: 9783639137873
Editorial: VDM Verlag Dr. Müller, 2009

Sinopsis

The numerical approximation of solutions of ordinary differential equations played an important role in Numerical Analysis and still continues to be an active field of research. In this book we are mainly concerned with the numerical solution of the first-order system of nonlinear two-point boundary value problems. We will focus on the problem of solving singular perturbation problems since this has for many years been a source of difficulty to applied mathematicians, engineers and numerical analysts alike. Firstly, we consider deferred correction schemes based on Mono-Implicit Runge-Kutta (MIRK) and Lobatto formulae. As is to be expected, the scheme based on Lobatto formulae, which are implicit, is more stable than the scheme based on MIRK formulae which are explicit. Secondly, we construct high order interpolants to provide the continuous extension of the discrete solution. It will consider the construction of both explicit and implicit interpolants. The estimation of conditioning numbers is also discussed and used to develop mesh selection algorithms which will be appropriate for solving stiff linear and nonlinear boundary value problems.

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Reseña del editor

The numerical approximation of solutions of ordinary differential equations played an important role in Numerical Analysis and still continues to be an active field of research. In this book we are mainly concerned with the numerical solution of the first-order system of nonlinear two-point boundary value problems. We will focus on the problem of solving singular perturbation problems since this has for many years been a source of difficulty to applied mathematicians, engineers and numerical analysts alike. Firstly, we consider deferred correction schemes based on Mono-Implicit Runge-Kutta (MIRK) and Lobatto formulae. As is to be expected, the scheme based on Lobatto formulae, which are implicit, is more stable than the scheme based on MIRK formulae which are explicit. Secondly, we construct high order interpolants to provide the continuous extension of the discrete solution. It will consider the construction of both explicit and implicit interpolants. The estimation of conditioning numbers is also discussed and used to develop mesh selection algorithms which will be appropriate for solving stiff linear and nonlinear boundary value problems.

Biografía del autor

Studied Numerical Analysis at Imperial College London, University of London, UK, 2001-2005. Assistant Professor at Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia.

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Editorial
VDM Verlag Dr. Müller
Año de publicación
2009
Idioma
Inglés
ISBN 10 
3639137876
ISBN 13 
9783639137873
Encuadernación
Tapa blanda
Número de páginas
212
Contacto del fabricante
no disponible
Persona responsable
no disponible