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This book presents methods for the computational solution of
differential equations, both ordinary and partial, time-dependent
and steady-state. Finite difference methods are introduced and
analyzed in the first four chapters, and finite element methods are
studied in chapter five. A very general-purpose and widely-used
finite element program, PDE2D, which implements many of the methods
studied in the earlier chapters, is presented and documented in
Appendix A.The book contains the relevant theory and error analysis
for most of the methods studied, but also emphasizes the practical
aspects involved in implementing the methods. Students using this
book will actually see and write programs (FORTRAN or MATLAB) for
solving ordinary and partial differential equations, using both
finite differences and finite elements. In addition, they will be
able to solve very difficult partial differential equations using
the software PDE2D, presented in Appendix A. PDE2D solves very
general steady-state, time-dependent and eigenvalue PDE systems, in
1D intervals, general 2D regions, and a wide range of simple 3D
regions.The Windows version of PDE2D comes free with every purchase
of this book. More information at www.pde2d.com/contact.
This book presents methods for the computational solution of
differential equations, both ordinary and partial, time-dependent
and steady-state. Finite difference methods are introduced and
analyzed in the first four chapters, and finite element methods are
studied in chapter five. A very general-purpose and widely-used
finite element program, PDE2D, which implements many of the methods
studied in the earlier chapters, is presented and documented in
Appendix A.The book contains the relevant theory and error analysis
for most of the methods studied, but also emphasizes the practical
aspects involved in implementing the methods. Students using this
book will actually see and write programs (FORTRAN or MATLAB) for
solving ordinary and partial differential equations, using both
finite differences and finite elements. In addition, they will be
able to solve very difficult partial differential equations using
the software PDE2D, presented in Appendix A. PDE2D solves very
general steady-state, time-dependent and eigenvalue PDE systems, in
1D intervals, general 2D regions, and a wide range of simple 3D
regions.The Windows version of PDE2D comes free with every purchase
of this book. More information at www.pde2d.com/contact.
This book presents methods for the computational solution of some
important problems of linear algebra: linear systems, linear least
squares problems, eigenvalue problems, and linear programming
problems. The book also includes a chapter on the fast Fourier
transform and a very practical introduction to the solution of
linear algebra problems on modern supercomputers.The book contains
the relevant theory for most of the methods employed. It also
emphasizes the practical aspects involved in implementing the
methods. Students using this book will actually see and write
programs for solving linear algebraic problems. Highly readable
FORTRAN and MATLAB codes are presented which solve all of the main
problems studied.
This book presents methods for the computational solution of some
important problems of linear algebra: linear systems, linear least
squares problems, eigenvalue problems, and linear programming
problems. The book also includes a chapter on the fast Fourier
transform and a very practical introduction to the solution of
linear algebra problems on modern supercomputers.The book contains
the relevant theory for most of the methods employed. It also
emphasizes the practical aspects involved in implementing the
methods. Students using this book will actually see and write
programs for solving linear algebraic problems. Highly readable
FORTRAN and MATLAB codes are presented which solve all of the main
problems studied.
This text can be used for two quite different purposes. It can be
used as a reference book for the PDElPROTRAN user. who wishes to
know more about the methods employed by PDE/PROTRAN Edition 1 (or
its predecessor, TWODEPEP) in solving two-dimensional partial
differential equations. However, because PDE/PROTRAN solves such a
wide class of problems, an outline of the algorithms contained in
PDElPROTRAN is also quite suitable as a text for an introductory
graduate level finite element course. Algorithms which solve
elliptic, parabolic, hyperbolic, and eigenvalue partial
differential equation problems are pre sented, as are techniques
appropriate for treatment of singularities, curved boundaries,
nonsymmetric and nonlinear problems, and systems of PDEs. Direct
and iterative linear equation solvers are studied. Although the
text emphasizes those algorithms which are actually implemented in
PDEI PROTRAN, and does not discuss in detail one- and
three-dimensional problems, or collocation and least squares finite
element methods, for example, many of the most commonly used
techniques are studied in detail. Algorithms applicable to general
problems are naturally emphasized, and not special purpose
algorithms which may be more efficient for specialized problems,
such as Laplace's equation. It can be argued, however, that the
student will better understand the finite element method after
seeing the details of one successful implementation than after
seeing a broad overview of the many types of elements, linear
equation solvers, and other options in existence."
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