Mathematical Foundation of the Boundary Integro-Differential Equation Method (Hardcover)

Houde Han

ISBN 10: 9819510872 / ISBN 13: 9789819510870

Published by Springer Verlag, Singapore, Singapore, 2026

About this Item

Hardcover. The book focuses on the mathematical foundations of boundary integro-differential equation method, with a primary focus on reducing the hypersingular integrals in traditional boundary integral equations into boundary integro-differential equations with weak singularities. It briefly introduces the theory of distributions, while the boundary integral equations method is grounded in the fundamental solutions of linear partial differential equations, hence a relatively detailed exposition of the fundamental solutions of differential equations is also provided. In the subsequent chapters, the authors sequentially discuss the boundary integro-differential equation methods and theories for Laplace equation, Helmholtz equation, Navier equations, Stokes equations, among others. Furthermore, the book addresses the boundary integro-differential equation method for certain nonlinear problems, such as thermal radiation, variational inequalities, and Steklov eigenvalue problems. Lastly, it explores the symmetric coupling issues between finite element and boundary element methods. The book focuses on the mathematical foundations of boundary integro-differential equation method, with a primary focus on reducing the hypersingular integrals in traditional boundary integral equations into boundary integro-differential equations with weak singularities. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Seller Inventory # 9789819510870

Bibliographic Details

• Title: Mathematical Foundation of the Boundary Integro-Differential Equation Method (Hardcover)
• Publisher: Springer Verlag, Singapore, Singapore
• Publication Date: 2026
• Language: English
• ISBN 10: 9819510872
• ISBN 13: 9789819510870
• Binding: Hardcover
• Condition: new

About this title

Synopsis

The book focuses on  the mathematical foundations of boundary integro-differential equation method, with a primary focus on reducing the hypersingular integrals in traditional boundary integral equations into boundary integro-differential equations with weak singularities. It briefly introduces the theory of distributions, while the boundary integral equations method is grounded in the fundamental solutions of linear partial differential equations, hence a relatively detailed exposition of the fundamental solutions of differential equations is also provided. In the subsequent chapters, the authors sequentially discuss the boundary integro-differential equation methods and theories for Laplace equation, Helmholtz equation, Navier equations, Stokes equations, among others. Furthermore, the book addresses the boundary integro-differential equation method for certain nonlinear problems, such as thermal radiation, variational inequalities, and Steklov eigenvalue problems. Lastly, it explores the symmetric coupling issues between finite element and boundary element methods.

About the Author

Han Houde is a professor at Tsinghua University who has devoted himself to the teaching and scientific research of computational mathematics. He has achieved significant breakthroughs in the study of numerical solutions of partial differential equations, demonstrating a series of creative research results. In particular, he has made important contributions to the numerical solutions of partial differential equations on unbounded domains and the coupling method of the finite element method and boundary element method. Additionally, he has contributed to the numerical solutions of boundary integral-differential equations and variational inequalities problems, as well as the numerical solutions of singular perturbation problems, ill-posed problems, and infinite element methods.

Yin Dongsheng is an associate professor at Tsinghua University whose research interest is mainly focused on high frequency waves, partial differential equations on unbounded domains, and fractional differential equations.