02795nam a22003974u 4500 10.1002/9781394276660 Wiley 20251030120320.0 cr nn 008mam|a 240313t2024||||xxu fs| |0|| 0|eng|| 9781394276660 electronic 10.1002/9781394276660 doi eng Makarov, Volodymyr aut 92257 Traditional Functional‐Discrete Methods for the Problems of Mathematical Physics New Aspects [electronic resource] Volodymyr Makarov, Nataliya Mayko 1 Wiley 2024 Wiley 2024 352pp.; text txt rdacontent computer c rdamedia online resource cr rdacarrier text file rdaft PDF 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. Mathematical & Computational Physics 91336 Physics Special Topics 91611 Theoretical Physics 92258 mathematical physics; weight functions; boundary of the domain; elliptic equations; parabolic equations; mesh schemes; fractional derivatives; Cayley transform method; abstract differential equations; Hilbert spaces; Banach spaces; universality; convenient implementation Mayko, Nataliya aut 92259 Printed edition: 9781786309334 https://doi.org/10.1002/9781394276660 Wiley Online Library https://onlinelibrary.wiley.com/action/showBook?doi=10.1002%2F9781394276660 Wiley Online Library Cover Image https://onlinelibrary.wiley.com/cms/asset/047b39a8-3936-41a5-8c43-fc9f966fa24f/9781394276660.cover.gif Wiley Online Library 67287 67287