Numerical Methods - 535.766

Most problems encountered in engineering and physics applications involve the solution of partial differential equations (PDEs). The analytical solution of PDEs is not generally available and one viable way to find the particular solution is by using numerical methods. Numerical methods enable us to find a numerical solution of the PDE by converting the PDE into a set of algebraic equations. To obtain a reliable and accurate numerical solution of the PDE, however, one should apply an appropriate numerical method with proper parameters depending on the types and properties of the PDE. While a number of tools to find the numerical solutions are available these days, the knowledge on the numerical methods will greatly help you to choose the right tool and set the correct parameters. In this course, a comprehensive introduction to the numerical methods for solving PDEs encountered in engineering and physics will be given. Mathematical analyses to identify the types and properties of the PDEs and the way to choose the proper numerical method to solve the given PDE will be introduced. Assessments of the stability and accuracy of each numerical method will also be discussed. For hands-on experience on applying the numerical methods, MATLAB or Python programming will be used for homework assignments and the final project. The knowledge you obtain throughout this course will make you more confident in applying numerical methods to deal with complex mathematical problems you may encounter in your career.