Traditional Functional-Discrete Methods for the Problems of Mathematical Physics

Download or read book Traditional Functional-Discrete Methods for the Problems of Mathematical Physics written by Volodymyr Makarov and published by John Wiley & Sons. This book was released on 2024-04-02 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the construction and study of approximate methods for solving mathematical physics problems in canonical domains. It focuses on obtaining weighted a priori estimates of the accuracy of these methods while also considering the influence of boundary and initial conditions. This influence is quantified by means of suitable weight functions that characterize the distance of an inner point to the boundary of the domain. New results are presented on boundary and initial effects for the finite difference method for elliptic and parabolic equations, mesh schemes for equations with fractional derivatives, and the Cayley transform method for abstract differential equations in Hilbert and Banach spaces. Due to their universality and convenient implementation, the algorithms discussed throughout can be used to solve a wide range of actual problems in science and technology. The book is intended for scientists, university teachers, and graduate and postgraduate students who specialize in the field of numerical analysis.