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"Artificial Boundary Method" systematically introduces the artificial boundary method for the numerical solutions of partial differential equations in unbounded domains. Detailed discussions treat different types of problems, including Laplace, Helmholtz, heat, Schrodinger, and Navier and Stokes equations. Both numerical methods and error analysis are discussed. The book is intended for researchers working in the fields of computational mathematics and mechanical engineering.
Prof. Houde Han works at Tsinghua University, China; Prof. Xiaonan Wu works at Hong Kong Baptist University,...

This book examines holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel. It opens perspectives on several active areas of research in complex, Kahler and symplectic geometry. A large number of applications are also included, such as an analytic proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, compactification of complete Kahler manifolds of pinched negative curvature, Berezin-Toeplitz quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer analytic...

This book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts.

In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE boundary value problems for different sets of derivative products (vanilla and exotic options, and interest rate derivatives). For many option problems, the analytic solutions are also derived with...

This book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts.

In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE boundary value problems for different sets of derivative products (vanilla and exotic options, and interest rate derivatives). For many option problems, the analytic solutions are also derived with...