In 2024, the Springer Publishing Company issued the digital edition of the monograph entitled “High-order finite difference and finite element methods for solving some partial differential equations” by scientists of the Laboratory of Information Technologies and Laboratory of Theoretical Physics at JINR, Mongolian University of Science and Technology, and Institute of Mathematics and Digital Technology of the Mongolian Academy of Sciences. The monograph was released as part of the book series titled “Synthesis Lectures on Engineering, Science, and Technology” and based on the results of collaborative research.

The monograph is devoted to the construction of the high-order finite difference and finite element methods for numerical solving multidimensional boundary-value problems (BVPs) for different partial differential equations, in particular, linear Helmholtz and wave equations, nonlinear Burgers’ equations, and elliptic (Schrödinger) equation.

Despite the methods’ long history, particularly in terms of the development of their theoretical background, there is still a number of unanswered questions regarding their constructive implementation in numerical solving of the multidimensional BVPs with additional requirement on physical parameters or desirable properties of its approximate solutions. Over the last two decades, many papers on this topic have been published, proposing new constructive approaches to numerically solving the multidimensional BVPs. These works require collection and systematisation.

The book will be useful to readers, graduate students, and researchers interested in computational physics, applied mathematics, numerical analysis, and applied sciences.

The authors of the monograph: Ulziibayar Vandandoo, Tugal Zhanlav, Ochbadrakh Chuluunbaatar, Alexander Gusev, Sergue Vinitsky, Galmandakh Chuluunbaatar.