Special Issue on Finite Difference Methods: Recent Developments and Applications in Computational Science
• 大类 : 工程技术 - 4区
• 小类 : 计算机：跨学科应用 - 4区
• 小类 : 计算机：理论方法 - 3区
Computational Science is a rapidly growing interdisciplinary field concerned with constructing mathematical models, numerical approximations of forward and inverse problems, quantitative analysis techniques, and using advanced computing capabilities to analyze, investigate and solve a wide range of complex problems in the natural and social sciences, medicine, and engineering, among others.
Finite difference approximations of differential equations are one of the oldest and simplest methods which are frequently used for computing approximate solutions of the underlying equations modeling complex phenomenon. With the availability of ever more powerful computational resources, the large but finite algebraic system of equations arising from finite difference approximations can be easily solved on present day computers, and the resulting efficient algorithms provide gold standards to beat for other approximation techniques.
Modeling and simulation tools based on Finite Difference techniques find increasing applications not only in fundamental research, but also in several real-world applications. However, the simplicity and efficiency of Finite Difference Methods comes at the cost of reduced accuracy and stability in the approximation of problems involving heterogenieties and nonsmooth interfaces.
The objective of this special issue is to present recent important developments in the construction, analysis and simulation of approximation techniques based on the Finite Difference Method (FDM) that address these and other limitations of the FDMs and provide efficient solutions to advance research in this area. High-quality original contributions to this special issue are invited from researchers working in this area.
Potential topics include but are not limited to the following:
· (High order) FDMs for Elliptic, Parabolic and Hyperbolic Problems
· (High order) FDMs for Initial and Boundary Value Problems