Synopsis
Master numerical PDEs with the method of lines and gain practical, hands-on skills.
This book explains how to solve partial differential equations by first discretizing space and then integrating in time. It covers the range of spatial discretizations, how to handle boundary conditions, and how to choose stable, accurate time-stepping methods. A practical FORTRAN package named MOLID is described, guiding users to set up problems and let the software pick suitable solvers, with options to override choices when needed. The text mixes theory with concrete examples, showing how to compare approaches and judge efficiency and accuracy.
Highlights include clear guidance on keeping essential PDE properties in the discrete model, discussions of stiffness and multistep methods, and numerous numerical examples that illuminate both hyperbolic and parabolic problems. The material is accessible to scientists with limited computing experience and aims to help them solve fairly complex problems efficiently.
- Clear explanation of space discretization and boundary conditions for common PDEs
- Practical guidance on stability, convergence, and time integration
- Discussion of computational efficiency and solver choices, including iterative and Jacobian approaches
- Hands-on examples using the MOLID package to compare numerical methods
Ideal for readers of engineering and applied math who want a reliable, approachable path to solving PDEs numerically.
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The Method of Lines Solution of Partial Differential Equations
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Paperback. Condition: New. Print on Demand. This book delves into the intricacies of the method of lines (MOL), a powerful technique for approximating solutions to partial differential equations (PDEs). The author meticulously examines various strategies for solving initial boundary value problems for PDEs, providing a detailed analysis of both spatial and temporal discretization methods. Building on the historical context of numerical methods for solving PDEs, the book explores how to optimize the MOL by carefully balancing spatial and temporal errors. It emphasizes the importance of choosing efficient combinations of spatial and temporal methods to achieve a desired level of accuracy with minimal computational effort. The book goes into considerable detail about the selection of appropriate ODE integration methods, focusing on multistep methods that are well-suited for handling the stiffness inherent in many PDE problems. The author then presents a practical implementation of the MOL, describing a user-friendly FORTRAN subroutine package called MOLlD that allows scientists and engineers to efficiently solve a wide range of PDEs. The book includes a collection of numerical examples showcasing the package's capabilities and limitations, demonstrating the effectiveness of various MOL techniques for different types of PDEs. Ultimately, this book provides a comprehensive and accessible guide to the method of lines, offering valuable insights into the theoretical underpinnings and practical applications of this important numerical tool for solving PDEs. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781330357095_0
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The Method of Lines Solution of Partial Differential Equations Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781330357095
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