LIMbook
swMATH ID:  14520 
Software Authors:  Brugnano, Luigi; Iavernaro, Felice 
Description:  Line Integral Methods for Conservative Problems. The book explains the numerical solution of differential equations within the framework of geometric integration, a branch of numerical analysis that devises numerical methods able to reproduce (in the discrete solution) relevant geometric properties of the continuous vector field. The book focuses on a large set of differential systems named conservative problems, particularly Hamiltonian systems. Assuming only basic knowledge of numerical quadrature and RungeKutta methods, this selfcontained book begins with an introduction to the line integral methods. It describes numerous Hamiltonian problems encountered in a variety of applications and presents theoretical results concerning the main instance of line integral methods: the energyconserving RungeKutta methods, also known as Hamiltonian boundary value methods (HBVMs). The authors go on to address the implementation of HBVMs in order to recover in the numerical solution what was expected from the theory. The book also covers the application of HBVMs to handle the numerical solution of Hamiltonian partial differential equations (PDEs) and explores extensions of the energyconserving methods. With many examples of applications, this book provides an accessible guide to the subject yet gives you enough details to allow concrete use of the methods. MATLAB codes for implementing the methods are available online 
Homepage:  http://web.math.unifi.it/users/brugnano/LIMbook/software.html 
Dependencies:  Matlab 
Related Software:  BiMD; BiM; RODAS; Mulprec; Matlab; HLLE; Expint; diffEq; BvpSolve; mftoolbox; GPELab; Taylor; TIDES; ADiGator; LIEDRIVERS; DiffSharp; MATLAB ODE suite; DNAD; ode23s; ode113 
Referenced in:  63 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Line integral methods for conservative problems. Zbl 1335.65097 Brugnano, Luigi; Iavernaro, Felice 
2016

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Referenced by 78 Authors
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Referenced in 22 Serials
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