Differential And Difference Equations With Applications

Authors: Qin, Yuming
Collects integral and discrete inequalities established by many different authors
Presents some integral and discrete inequalities and their applications in (partial) differential equations, integral equations and discrete equations
Introduces Gronwall-Bellman, Henry, Bihari and Ou-Yang inequalities
Presents numerous inequalities, which cannot be found in other books

This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions.

This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions.

Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields in much the same way as the classical algebraic geometry arose from the study of polynomial equations with numerical coefficients. The first stage of the development of the theory is associated with its founder J. F. Ritt (1893 - 1951) and R. Cohn whose book Difference Algebra (1965) remained the only fundamental monograph on the subject for many years.