Questions


Below you will find some additional question that may help you better digest the material for this course. They should be particularly useful to those who will choose MATH745 as a part of their Comprehensive Exam.

Analyze dispersive errors (i.e., related to the mismatch of the phases in the exact and approximate solutions) in the leapfrog scheme
Hint - focus on the case of an equation with purely imaginary coefficients for values of h that give stable solutions

Derive a class of second-order accurate Runge-Kutta methods (RK2)
Hint - start with the formula given on p. 35 in the transparencies with k_1 and k_2 only (i.e., k_3=0, ...)

Derive the formulae characterizing the differentiation matrices of the first and second order for the case of interpolation using trigonometric series (consider both even and odd collocations)

Elaborate on the relation between the pseudospectral Galerkin and collocation approaches to solution of a nonlinear PDE.