- Email: [email protected]
Computational methods for partial differential equations
for discrete sequential estimation’, Academic Press, New York and London, 1911 l&lath, T. ‘Linear systems’, PrenticeHall, Englewood Cliffs, NJ, 1980 Rosenbrock, H. H. ‘State-space and multivariable theory’, Nelson, London, 1970 Wolovich, W. A. ‘Linear multivariable systems’, Springer Verlag, New York, 1974 Bellman, R. ‘Introduction to matrix analysis’ (2nd edn), McGraw-Hill, New York, 1970 Mathematical quality: (Vol.
12,
applied Edited
modelling
of water
streams, lakes and reservoirs
I IASA international
series on
systems analysis) by G. T. Orlob
John Wiley,
Chichester,
UK,
1983,
518 pp., f52.75
To be honest, my first reaction to hearing of the publication of this book was the price. At over c50 it must only be destined for library acquisition lists; and even then in these times of shrinking budgets, any university librarian will need a high recommendation from a large number of academics. Not that this book will not receive such support. The modelling talent arrayed in this volume by the edtitor, Dr Orlob, is indeed substantial and their contributions are well received. However, by its very nature of concatenating several areas of expertise it cannot pretend to be comprehensive in its compass. Despite this inherent limitation, the material that is included is interesting and attempts to strike a balance between modelling and models. This is especially apparent in the preliminary chapters where there is some useful discussion on the process of modelling, including the vital (and often overlooked) verification and validations stages. Chapter 3 provides the bridge between the earlier chapters centred on modelling through to the later chapters which concentrate more on the physics and conceptualizations of a wide range of models. Chapters 5 and 6 deal with rivers and streams and Chapters 7, 8 and 9 with lakes and reservoirs. Chapter 10 concentrates on one specific aspect: the pollution problem resulting from toxic spills. The final two chapters deal with the calibration and validation stages together with a more management orientated objective and the book is rounded off with an editorial on the future prospects of water quality modelling. Although the editing has resulted in a common notation throughout the book insofar as this is reasonable, there is no common reference list which I would have liked to have seen. The collecting together of references at the end of each chapter serves, to
308
Appl.
Math.
Modelling,
1985,
Vol.
my mind, to destroy the continuity of the work and suggest to the reader that the connection and overlapping between chapters is less strong than it in fact is. Secondly and sadly, apparently with an inevitability in a work of collected papers such as this, the book was out-of-date when it was published. This results partly from the impossibility of encouraging all the authors to write and submit their manuscripts at the same time. Nevertheless the fact that in a book published in 1983 (and therefore presumably written by 1982) the latest literature reference in almost all the chapters is 1979. (There are in fact a few exceptions to this but these relate largely to the authors’ own published work, or that accepted for publication, in 1980 or 198 1). The emphasis apparent to modellers at the time of writing was, I suspect, different to that of the present day; so that my notes on reading the book relating to the omission of certain key topics such as the effects on thermal stratification due to hydraulic forcing of buoyant and non-buoyant inflows and the use of mathematical models for the management of lakes and reservoirs by the implementation of destratification techniques may be a simple reflection of this temporal discrepancy. With this caveat, I would suggest that in this volume is much work which deserves to be studied and we can be grateful for Dr Orlob for bringing together this vast amount of modelling and model information in this expanding area of water quality modelling. Certainly if the International Drinking Water Supply and Sanitation Decade is to have any success in developing water resources for the whole world, then some of the results of the models described here should be of a wider significance. B. Henderson-Sellers Computational differential
methods
for partial
equations
E. H. Twizell Ellis Horwood,
Chichester,
UK,
1984,
pp. 276, f27.50
This text attempts to cover a range of numerical techniques for the solution of the standard cases of second order elliptic, hyperbolic and parabolic equations in up to two independent space variables. After an introductory chapter on basic numerical linear algebra and discretation of derivatives, finite difference and finite element methods for elliptic equations are discussed, followed by chapters on finite difference techniques and characteristic methods for hyperbolic equations, with a brief reference to the Galerkin method, and finite difference methods for parabolic equations.
9, August
The book could be considerably improved by the inclusion of a relatively small amount of material, the omission of some material which does not appear to be particularly relevant and a more thorough proof reading. For example, in the introduction, the power method for finding dominant eigenvalues is described and yet in the section on elliptic equations the eigenvalues for tridiagonal matrices are quoted without any discussion. In this same section it would be of great assistance to have uniqueness results for Dirichlet and Neumann problems described. At the end of the Neumann section it is stated (nearly) that the discrete Neumann problem has a singular matrix with no clue as to whether this is a result of the discretization or a reflection of the original problem. In several instances, statements are made at the end of a problem saying that a solution of a problem has been found. What is really meant is that a numerical solution, possibly approximate, has been found to a discretization of the original problem. The irregular boundary problem is a good example; presentation of the numerical results would have been of great interest. The abstract theory presented in the introduction to the finite element method barely seems to be used as convergence and error analysis is not discussed. The chapter is marred by a number of misprints, the most blatant being the mis-statement of the stiffness matrix for the linear triangular discretization, of the Laplace operator. The spaces C’>J do not appear to have been defined. The choice of element types, I find a little strange, there being no discussion of the one-dimensional hat functions or eight- or ninenoded quadrilateral elements, the latter performing probably as well as the rather non-standard rational functions, on the circle problem (?). The use of Pad6 approximants in the discussion of time discretization in the hyperbolic and parabolic sections is an elegant approach. Some confusion, however, appears in 4.8 and 4.10 when defining the governing equations, where the discussion is relevant to quasilinear equations and not the types named. It is interesting to see the multitime level and extrapolation procedures in an accessible form and the use of Pad& approximants. This is certainly an advance from Smith’s classic finite difference text; It is a pity that the remainder does not match this presentation. I would find difficulty recommending the text for general student use.
K. Barrett
12,
applied Edited
modelling
of water
streams, lakes and reservoirs
I IASA international
series on
systems analysis) by G. T. Orlob
John Wiley,
Chichester,
UK,
1983,
518 pp., f52.75
To be honest, my first reaction to hearing of the publication of this book was the price. At over c50 it must only be destined for library acquisition lists; and even then in these times of shrinking budgets, any university librarian will need a high recommendation from a large number of academics. Not that this book will not receive such support. The modelling talent arrayed in this volume by the edtitor, Dr Orlob, is indeed substantial and their contributions are well received. However, by its very nature of concatenating several areas of expertise it cannot pretend to be comprehensive in its compass. Despite this inherent limitation, the material that is included is interesting and attempts to strike a balance between modelling and models. This is especially apparent in the preliminary chapters where there is some useful discussion on the process of modelling, including the vital (and often overlooked) verification and validations stages. Chapter 3 provides the bridge between the earlier chapters centred on modelling through to the later chapters which concentrate more on the physics and conceptualizations of a wide range of models. Chapters 5 and 6 deal with rivers and streams and Chapters 7, 8 and 9 with lakes and reservoirs. Chapter 10 concentrates on one specific aspect: the pollution problem resulting from toxic spills. The final two chapters deal with the calibration and validation stages together with a more management orientated objective and the book is rounded off with an editorial on the future prospects of water quality modelling. Although the editing has resulted in a common notation throughout the book insofar as this is reasonable, there is no common reference list which I would have liked to have seen. The collecting together of references at the end of each chapter serves, to
308
Appl.
Math.
Modelling,
1985,
Vol.
my mind, to destroy the continuity of the work and suggest to the reader that the connection and overlapping between chapters is less strong than it in fact is. Secondly and sadly, apparently with an inevitability in a work of collected papers such as this, the book was out-of-date when it was published. This results partly from the impossibility of encouraging all the authors to write and submit their manuscripts at the same time. Nevertheless the fact that in a book published in 1983 (and therefore presumably written by 1982) the latest literature reference in almost all the chapters is 1979. (There are in fact a few exceptions to this but these relate largely to the authors’ own published work, or that accepted for publication, in 1980 or 198 1). The emphasis apparent to modellers at the time of writing was, I suspect, different to that of the present day; so that my notes on reading the book relating to the omission of certain key topics such as the effects on thermal stratification due to hydraulic forcing of buoyant and non-buoyant inflows and the use of mathematical models for the management of lakes and reservoirs by the implementation of destratification techniques may be a simple reflection of this temporal discrepancy. With this caveat, I would suggest that in this volume is much work which deserves to be studied and we can be grateful for Dr Orlob for bringing together this vast amount of modelling and model information in this expanding area of water quality modelling. Certainly if the International Drinking Water Supply and Sanitation Decade is to have any success in developing water resources for the whole world, then some of the results of the models described here should be of a wider significance. B. Henderson-Sellers Computational differential
methods
for partial
equations
E. H. Twizell Ellis Horwood,
Chichester,
UK,
1984,
pp. 276, f27.50
This text attempts to cover a range of numerical techniques for the solution of the standard cases of second order elliptic, hyperbolic and parabolic equations in up to two independent space variables. After an introductory chapter on basic numerical linear algebra and discretation of derivatives, finite difference and finite element methods for elliptic equations are discussed, followed by chapters on finite difference techniques and characteristic methods for hyperbolic equations, with a brief reference to the Galerkin method, and finite difference methods for parabolic equations.
9, August
The book could be considerably improved by the inclusion of a relatively small amount of material, the omission of some material which does not appear to be particularly relevant and a more thorough proof reading. For example, in the introduction, the power method for finding dominant eigenvalues is described and yet in the section on elliptic equations the eigenvalues for tridiagonal matrices are quoted without any discussion. In this same section it would be of great assistance to have uniqueness results for Dirichlet and Neumann problems described. At the end of the Neumann section it is stated (nearly) that the discrete Neumann problem has a singular matrix with no clue as to whether this is a result of the discretization or a reflection of the original problem. In several instances, statements are made at the end of a problem saying that a solution of a problem has been found. What is really meant is that a numerical solution, possibly approximate, has been found to a discretization of the original problem. The irregular boundary problem is a good example; presentation of the numerical results would have been of great interest. The abstract theory presented in the introduction to the finite element method barely seems to be used as convergence and error analysis is not discussed. The chapter is marred by a number of misprints, the most blatant being the mis-statement of the stiffness matrix for the linear triangular discretization, of the Laplace operator. The spaces C’>J do not appear to have been defined. The choice of element types, I find a little strange, there being no discussion of the one-dimensional hat functions or eight- or ninenoded quadrilateral elements, the latter performing probably as well as the rather non-standard rational functions, on the circle problem (?). The use of Pad6 approximants in the discussion of time discretization in the hyperbolic and parabolic sections is an elegant approach. Some confusion, however, appears in 4.8 and 4.10 when defining the governing equations, where the discussion is relevant to quasilinear equations and not the types named. It is interesting to see the multitime level and extrapolation procedures in an accessible form and the use of Pad& approximants. This is certainly an advance from Smith’s classic finite difference text; It is a pity that the remainder does not match this presentation. I would find difficulty recommending the text for general student use.
K. Barrett