Unified Transform for Boundary Value Problems

This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives and discuss recent applications of the unified transform to the analysis and numerical modelling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method. The text covers a variety of aspects of the topic, including new theoretical results on linear and nonlinear evolutionary and elliptic problems, variational formulations for elliptic problems, and recent numerical applications based on the boundary element method and on the unified transform. The book is intended for applied and numerical research mathematicians and scientists working on the solution of boundary value problems in physics and engineering.

• Describes a novel and simple analytical method of unprecedented power for solving boundary value problems for linear PDEs
• Introduces simple techniques for the numerical solution of linear evolution and linear elliptic PDEs
• Reviews the state of the art on boundary element methods