By Vladimir Dorodnitsyn
Intended for researchers, numerical analysts, and graduate scholars in a number of fields of utilized arithmetic, physics, mechanics, and engineering sciences, Applications of Lie teams to distinction Equations is the 1st e-book to supply a scientific building of invariant distinction schemes for nonlinear differential equations. A advisor to equipment and ends up in a brand new region of software of Lie teams to distinction equations, distinction meshes (lattices), and distinction functionals, this publication makes a speciality of the upkeep of entire symmetry of unique differential equations in numerical schemes. This symmetry upkeep leads to symmetry relief of the variation version in addition to that of the unique partial differential equations and so as relief for traditional distinction equations.
A mammoth a part of the e-book is anxious with conservation legislation and primary integrals for distinction versions. The variational procedure and Noether kind theorems for distinction equations are provided within the framework of the Lagrangian and Hamiltonian formalism for distinction equations.
In addition, the ebook develops distinction mesh geometry in response to a symmetry team, simply because assorted symmetries are proven to require various geometric mesh buildings. the strategy of finite-difference invariants offers the mesh producing equation, any distinctive case of which promises the mesh invariance. a couple of examples of invariant meshes is gifted. specifically, and with various functions in numerics for non-stop media, that the majority evolution PDEs must be approximated on relocating meshes.
Based at the constructed approach to finite-difference invariants, the sensible sections of the ebook current dozens of examples of invariant schemes and meshes for physics and mechanics. specifically, there are new examples of invariant schemes for second-order ODEs, for the linear and nonlinear warmth equation with a resource, and for recognized equations together with Burgers equation, the KdV equation, and the Schrödinger equation.
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