Faculty : Institute of Basic and Applied Sciences

School :

Course Description :

This course is primarily concerned with classes of problems and PDEs, types of boundary conditions, classes of numerical methods for PDEs, analysis of numerical methods for PDEs, errors, time, and memory. In this class, the student will deal with Boundary value problems: Elliptic PDEs (Finite difference methods, Finite element methods and overview of linear solvers for PDEs). Also, initial value problems: Parabolic and Hyperbolic PDEs (Parabolic PDEs, Finite difference methods, Hyperbol-ic PDEs, Finite difference methods, Convergence, Stability and Method of lines) are included. Advanced and parallel methods for PDEs (Paral-lel methods for BVPs, Domain decomposition, Schur complement method, Schwarz alternating method, Multigrid method, Fast Fourier Transform solvers), software development.

Faculty : Institute of Basic and Applied Sciences

School :

Course Description :

The aim of this course is to provide students with the fundamentals of parallel computing, linear systems (direct methods such as Gauss elim-ination, LU factorization, symmetric and symmetric positive definite ma-trices, banded systems, pivoting in banded systems, tridiagonal sys-tems, banded systems, partitioning methods) and linear systems (itera-tive methods such as Jacobi and Gauss-Seidel methods, CG method ,preconditioning , preconditioned CG method, application to the GS, SOR and SSOR methods, Block iterative methods).

Faculty : Institute of Basic and Applied Sciences

School :

Course Description :

The main topic of the course is the study of partial differential equations (Schur complement method, arrowhead matrix, application to the 1D BVP, the use of CG for the solution of the Schur complement system, Schur complement method, application to the 2D BVP, Schwarz alter-nating (splitting) method, preconditioning, Multigrid method, FFT meth-ods, application to the 1D BVP, Tensor products of matrices).

Faculty : Institute of Basic and Applied Sciences

School :

Course Description :

This class aims to provide a basic theory of fractional differential equa-tions, Integral transform method for explicit solutions to fractional differ-ential equations, sequential linear differential equations of fractional order and system of fractional order differential equations. Partial differ-ential equations of fractional order. Also, numerical methods for solving fractional differential equations arising in science and engineering are considered.

Faculty : Institute of Basic and Applied Sciences

School :

Course Description :

Computational science and engineering has applications to a wide va-riety of fields, from physics to engineering and medicine. This is one of its most exciting aspects that it brings researchers from many disciplines together with a common language. The class is concerned with devel-opment and analysis of algorithms used in the solution of science and engineering problems. Numerical analysis of discretization schemes for partial differential equations. Also, a survey of finite difference, finite element, finite volume and spectral approximations for the numerical solution of the incompressible and compressible flow, Euler and Navier-Stokes equations, including shock-capturing methods are concluded.