Numerical Methods for the Solution of Partial Differential Equations: A Review

The main purpose of the research project: Radial Basis Function Methods for the Solution of PDE, is to study, research and develop numerical algorithms to solve partial differential equations by means of radial basis function methods. These techniques, which were developed during the last decade, have proved to be a powerful tool for the solution of real life problems of great scale.

This project is essentially interdisciplinary; we aim to build mathematical models of problems, which belongs to different areas of knowledge. An important objective of this project is to develop a flexible, object oriented library, which let the user to apply and implement these numerical techniques. Our purpose, is not only to use “black boxes” to solve PDE problems, but instead, to boost the implementation and developement of computational systems for  these new methods

This project has tree main objectives, which can be classified into: research, education and computer systems development.

  • In the field of research, we aim to investigate numerical algorithms both form the theoretical and applied point of view. The application of these techniques to different areas of knowledge is also an important purpose of this point.
  • Within the educationalobjective, we incorporate simple codes as well as their explanation, which aims to help students and lecturers to understand and/or teach these new numerical methods.

The third objective is to build a free software library whose flexibility let the user to incorporate new routines or algorithms. 


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