By Luigi Brugnano,Felice Iavernaro
Line critical tools for Conservative Problems explains the numerical resolution of differential equations in the framework of geometric integration, a department of numerical research that devises numerical tools in a position to reproduce (in the discrete resolution) appropriate geometric houses of the continual vector box. The publication makes a speciality of a wide set of differential structures named conservative difficulties, relatively Hamiltonian systems.
Assuming in basic terms simple wisdom of numerical quadrature and Runge–Kutta tools, this self-contained ebook starts with an advent to the road imperative tools. It describes quite a few Hamiltonian difficulties encountered in quite a few functions and offers theoretical effects about the major example of line necessary equipment: the energy-conserving Runge–Kutta tools, often referred to as Hamiltonian boundary worth tools (HBVMs). The authors cross directly to handle the implementation of HBVMs which will get better within the numerical answer what was once anticipated from the speculation. The booklet additionally covers the applying of HBVMs to address the numerical resolution of Hamiltonian partial differential equations (PDEs) and explores extensions of the energy-conserving methods.
With many examples of functions, this e-book presents an available consultant to the topic but supplies sufficient information to permit concrete use of the equipment. MATLAB codes for enforcing the tools can be found online.
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Extra info for Line Integral Methods for Conservative Problems (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
Line Integral Methods for Conservative Problems (Chapman & Hall/CRC Monographs and Research Notes in Mathematics) by Luigi Brugnano,Felice Iavernaro