Accelerations As(MM) and Aco(MM) To Find Double Integrals Numerically

Evaluating Singular and Nearly Singular Integrals Numerically

Double Integrals and Iterated Integrals

Corresponding material in the book: Section 15.2, 15.3. Note: We are omitting the question types from the book that require three-dimensional visualization, i.e., those that require sketching figures in three dimensions to compute volumes. What students should definitely get: The procedure for computing double integrals over rectangles using iterated integrals, the procedure for computing doubl...

Fast, numerically stable computation of oscillatory integrals with stationary points

We present a numerically stable way to compute oscillatory integrals of the form ∫ 1 −1 f(x)e iωg(x) dx. For each additional frequency, only a small, well-conditioned linear system with a Hessenberg matrix must be solved, and the amount of work needed decreases as the frequency increases. Moreover, we can modify the method for computing oscillatory integrals with stationary points. This is the ...

SOLVING ODE’s NUMERICALLY WHILE PRESERVING ALL FIRST INTEGRALS

Using Discrete Gradient Methods (Quispel & Turner, J. Phys. A29 (1996) L341-L349) we construct integration methods that solve ordinary differential equations numerically while preserving all their first integrals (i.e. constants of the motion) exactly. 1 Department of Mathematics, La Trobe University, Bundoora, Melbourne, 3083, Australia. 2 E-mail: [email protected] 3 Instituut voor Theo...

From algebraic to analytic double product integrals

The algebraic theory of double product integrals and particularly its role in the quantisation of Lie bialgebras is described. When the underlying associative algebra is that of the Itô differentials of quantum stochastic calculus such product integrals are formally represented as operators which are infinite sums of iterated integrals in Fock space. In this paper we describe some of the analyt...