Final research paper for 21-660 Numerical Analysis, Fall 2014. This paper investigates some use cases of applying several numerical quadrature methods (namely, Newton-Cotes, Gaussian quadrature, and ...

Ordinary differential equations are ubiquitous in scientific computing. Solving exactly these equations is usually not possible, except for special cases, hence the use of numerical schemes to get a ...

Backward error analysis has become an important tool for understanding the long time behavior of numerical integration methods. This is true in particular for the integration of Hamiltonian systems ...

The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate-but ...

In those cases the Fundamental Theorem of Calculus cannot be applied and the values of the integral have to be approximated numerically. It is clear that when using numerical calculations, due to the ...

In particular, the integration of finite element methods, time-discretisation techniques and reconstruction approaches has facilitated more accurate simulation of complex, time-dependent phenomena.

Numerical Solution of Systems of Linear Equations, Iterative Methods Formulation and analysis of basic stationary methods e.g. Gauss-Jacobi, Gauss-Seidel. The numerical solution of Poisson's equation.