02685nam a22003734u 450000100220000000300060002200500170002800700150004500800410006002000300010102400310013104100080016210000280017024501580019825000060035626000160036226400160037830000120039433600260040633700260043233800360045834700210049434700080051552010510052365000410157465000270161565000240164265302760166670000250194277600360196785600640200385601020206785601420216910.1002/9781394276660Wiley20251030120320.0cr nn 008mam|a240313t2024||||xxu    fs|   |0|| 0|eng||  a9781394276660qelectronic7 a10.1002/97813942766602doi  aeng1 aMakarov, Volodymyr4aut10aTraditional Functional‐Discrete Methods for the Problems of Mathematical PhysicsbNew Aspectsh[electronic resource]cVolodymyr Makarov, Nataliya Mayko  a1  bWileyc2024 1bWileyc2024  a352pp.;  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext file2rdaft  bPDF  aThis 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. 4aMathematical & Computational Physics 4aPhysics Special Topics 4aTheoretical Physics00amathematical 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 implementation1 aMayko, Nataliya4aut08iPrinted edition:z978178630933440uhttps://doi.org/10.1002/9781394276660aWiley Online Library40uhttps://onlinelibrary.wiley.com/action/showBook?doi=10.1002%2F9781394276660aWiley Online Library423Cover Imageuhttps://onlinelibrary.wiley.com/cms/asset/047b39a8-3936-41a5-8c43-fc9f966fa24f/9781394276660.cover.gifaWiley Online Library