Discrete variational derivative method : a structurepreserving numerical method for partial differential equations /: a structurepreserving numerical method for partial differential equations. (©2011)

• Record Type: Book
• Further Information: Note: Daisuke Furihata, Takayasu Matsuo.
• Other Names: Furihata, Daisuke; Matsuo, Takayasu
• Contents: 1. Introduction and summary of this book An introductory example: the spinodal decomposition -- History -- Derivation of dissipative or conservative schemes advanced topics -- 2. Target partial differential equations -- Variational derivatives -- First-order real-valued PDEs -- First-order complex-valued PDEs -- Systems of first-order PDEs -- Second-order PDEs -- 3. Discrete variational derivative method -- Discrete symbols and formulas -- Procedure for first-order real-valued PDEs -- Procedure for first-order complex-valued PDEs -- Procedure for systems of first-order PDEs -- Procedure for second-order PDEs -- Preliminaries on discrete functional analysis -- 4. Applications -- Target PDEs 1 -- Target PDEs 2 -- Target PDEs 3 -- Target PDEs 4 -- Target PDEs 5 -- Target PDEs 7 -- Other equations -- 5. Advanced topic I: design of high-order schemes -- Orders of accuracy of schemes -- Spatially high-order schemes -- Temporally high-order schemes: composition method -- Temporally high-order schemes: high-order discrete variational derivatives -- 6. Advanced topic II: design of linearly-implicit schemes -- Basic idea for constructing linearly-implicit schemes -- Multiple-points discrete variational derivative -- Design of schemes -- Applications -- Remarks on the stability of linearly-implicit schemes -- 7. Advanced topic III: further remarks -- Solving system of nonlinear equations -- Switch to Galerkin framework -- Extension to non-rectangular meshes on 2D Region -- A. Semi-discrete schemes in space B -- Proof of Proposition 3.4.
• Publisher Details: Boca Raton, FL : Chapman and Hall/CRC
• Publication Date: 2011
• Copyright Date: 2011
• Extent: 1 online resource (xi, 376 pages), illustrations
• Subjects: 518.64 F984; Differential equations, Partial -- Numerical solutions; Nonlinear theories; Engineering mathematics; MATHEMATICS -- Numerical Analysis; Differential equations, Partial -- Numerical solutions; Engineering mathematics; Nonlinear theories; Electronic books
• Languages: English
• ISBNs: 9781420094466; 1420094467
• Related ISBNs: 9781420094459; 1420094459
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.