By Vladimir Dorodnitsyn
Intended for researchers, numerical analysts, and graduate scholars in numerous fields of utilized arithmetic, physics, mechanics, and engineering sciences, Applications of Lie teams to distinction Equations is the 1st booklet to supply a scientific development of invariant distinction schemes for nonlinear differential equations. A advisor to equipment and leads to a brand new quarter of software of Lie teams to distinction equations, distinction meshes (lattices), and distinction functionals, this publication specializes in the maintenance of whole symmetry of unique differential equations in numerical schemes. This symmetry protection leads to symmetry aid of the adaptation version besides that of the unique partial differential equations and so as aid for usual distinction equations.
A giant a part of the booklet is anxious with conservation legislation and primary integrals for distinction types. The variational technique and Noether style theorems for distinction equations are provided within the framework of the Lagrangian and Hamiltonian formalism for distinction equations.
In addition, the booklet develops distinction mesh geometry in line with a symmetry crew, simply because diversified symmetries are proven to require various geometric mesh constructions. the tactic of finite-difference invariants offers the mesh producing equation, any distinct case of which promises the mesh invariance. a few examples of invariant meshes is gifted. particularly, and with various purposes in numerics for non-stop media, that the majority evolution PDEs must be approximated on relocating meshes.
Based at the built approach to finite-difference invariants, the sensible sections of the e-book 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 famous equations together with Burgers equation, the KdV equation, and the Schrödinger equation.
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Applications of Lie Groups to Difference Equations (Differential and Integral Equations and Their Applications) by Vladimir Dorodnitsyn
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