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Khadijeh Nedaiasl

Phone: (+98) 24 33155053
Emails: nedaiasl@iasbs.ac.ir
knedaiasl85@gmail.com
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Position
Education
Ph.D

thesis on “Numerical Solution of Nonlinear Fredholm Integral Equation via Projection Methods”, Department of Mathematics, Iran University of Science and Technology (IUST),Tehran, Iran. (September, 2013).

Publications
Google Scholar
ResearchGate
Courses

This course will cover
  • Introduction to integarl equations

    • Types of integral equations: Volterra and Fredholm integral equatins of the first and second kind, Abel, Wiener Hopf, and Cauchy singular integral equations
    • Compact integral operators
    • The Fredholm alternative
  • Boundary integral equations. Green's identities and representation formulae in two and three dimensions
  • The Nystrom method: Error analysis and conditioning of the linear systems arising from integral equations
  • The projection (collocation and Galerkin) methods: Error analysis and conditioning of the linear systems arising from integral equations
  • An overview on the linear multistep methods for Volterra integral equation

There will be a homework assignment (with some programming) and also a term project based on relevant papers in the literature.

This course will cover
  • Introduction to PDEs

    • Classification of PDEs
    • The 1-D Heat Equations (Physical derivation)
    • Method of separable variable
    • Fourier Theory
  • Approximation by finite difference
  • Parabolic equations in one space variable
  • Numerical methods for parabolic equations
  • Hyperbolic equations in one space variable
  • Numerical methods for hyperbolic equations
  • Analysis of elliptic equations
  • Numerical methods for elliptic equations

There will be a homework assignment (with some programming) and also a term project based on relevant papers in the literature.

This course will be in two parts (I and II) and will cover
  • Machine Arithmetic and Related Matters

    • Floating Point Arithmetic and Achilles' Heel
    • Error Analysis
  • Approximation Theory

    • Preliminaries
    • The Approximation Theorem of Weirestrass
    • The General Approximation Problem
    • Orthogonal Polynomials
    • Uniform Approximation
    • Approximation in Pre-Hilbert Space
    • The Method of Least Squares
  • Interpolation

    • Interpolation as an Operator
    • Interpolation Methods and Remainders
    • Interpolation on Equidistant Points and Runge's Phenomenon
    • Convergence of Interpolating Polynomials
    • Interpolation by Splines
  • Numerical Integration

    • Interpolatory Quadrature
    • Gauss Quadrature
    • Special Quadrature Methods
    • Optimality and Convergence
  • Multivariable Approximation

    • The Haar-Mairhuber-Curtis theorem
    • Interpolation on rectangular grids
    • Interpolation on triangular grids
    • The Padua points

There will be a homework assignment (with some programming) and also a term project based on relevant papers in the literature.

Attended workshops and conferences
School of Fundamental and practice of finite elements

April 16- 20, 2018, Roscoff, France


Workshop on Integral Equations and Matrix Theory: Symbolic-Numeric Treatments

November 29-30, 2017, Tehran-Iran


CIMPA: Summer School on Multiscale Computational Methods and Error Control

July 10 - 21, 2017, IITK, India


Zurich Summer School on Numerical Methods for Wave Propagation

August 22-26, 2016, Zurich, Switzerland


The First Workshop on Finite Element Methods for PDEs

April 6-7, 2016, Sanandaj, Iran


IPM-Isfahan workshop on Numerical Analysis

May 30 - 31, 2015, Isfahan, Iran


The 2nd FINACT-IRAN Conference on Financial and Actuarial Mathematics

August 15-17, 2015, Tehran, Iran