The Method of Fractional Steps provides a rigorous mathematical framework for solving multidimensional problems. This book details the theory and application of the method of fractional steps, a technique developed by N. N. Yanenko for solving multidimensional problems of mathematical physics. It focuses on the decomposition of complex operators into simpler ones, enabling the solution of problems in multiple dimensions through a sequence of one-dimensional problems. The text explores the theoretical underpinnings and practical implementations of this method, particularly for parabolic and elliptic equations.

This seminal work by N. N. Yanenko is recognized as a foundational text in the field of numerical methods for solving partial differential equations. Its detailed exposition of the method of fractional steps has been influential in computational mathematics and physics. The book is regarded as a comprehensive resource for researchers and practitioners seeking to understand and apply advanced numerical techniques for complex problems. Its rigorous approach and thorough treatment of the subject matter solidify its place as a key reference in the discipline.