Essays about: "Chebyshev Collocation"

Found 2 essays containing the words Chebyshev Collocation.

  1. 1. Feigenbaum Scaling

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Janek Sendrowski; [2020]
    Keywords : Feigenbaum; Feigenbaum constant; Feigenbaum point; superstable; self-similarity; fractals; final-state diagram; logistic map; period-doubling operator; linearized period-doubling operator; Cantor set; Sharkovsky sequence; Chebyshev interpolation; stable manifold; unstable manifold; orbits; fixed points; scaling factor; pitchfork bifurcation; cobweb plot; renormalization; iterates; one-hump map; unimodal map; bifurcation cascade; Feigenbaum universality; chaos theory; spectrum; generalized Feigenvalues; bifurcation points; superstable points; fixed function; universal function; eigenvalues; eigenvectors; eigenfunctions; universality conditions; Schwarzian derivative; Newton’s method; power method; Arnoldi’s method; attractive fixed point; repellent fixed point; Banach fixed-point theorem; collocation method; functional analysis; topology;

    Abstract : In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. READ MORE

  3. 2. Evaluation of a least-squares radial basis function approximation method for solving the Black-Scholes equation for option pricing

    University essay from Institutionen för informationsteknologi

    Author : Cong Wang; [2012]
    Keywords : RBF; radial basis function; ill-conditioning; shape parameter; Black-Scholes equation; option pricing;

    Abstract : Radial basis function (RBF) approximation, is a new extremely powerful tool that is promising for high-dimensional problems, such as those arising from pricing of basket options using the Black-Scholes partial differential equation. The main problem for RBF methods have been ill-conditioning as the RBF shape parameter becomes small, corresponding to flat RBFs. READ MORE